2.1 Portuguese Exploration and Spanish Conquest
Learning Objectives
By the end of this section, you will be able to:
- Describe Portuguese exploration of the Atlantic and Spanish exploration of the Americas and the importance of these voyages to the developing Atlantic World
- Explain the importance of Spanish exploration of the Americas in the expansion of Spain’s empire and the development of Spanish Renaissance culture
Portuguese colonization of Atlantic islands in the 1400s inaugurated an era of aggressive European expansion across the Atlantic. In the 1500s, Spain surpassed Portugal as the dominant European power. This age of exploration and the subsequent creation of an Atlantic World marked the earliest phase of globalization, in which previously isolated groups—Africans, Native Americans, and Europeans—first came into contact with each other, sometimes with disastrous results.
PORTUGUESE EXPLORATION
Portugal’s Prince Henry the Navigator spearheaded his country’s exploration of Africa and the Atlantic in the 1400s. With his support, Portuguese mariners successfully navigated an eastward route to Africa, establishing a foothold there that became a foundation of their nation’s trade empire in the fifteenth and sixteenth centuries.
Portuguese mariners built an Atlantic empire by colonizing the Canary, Cape Verde, and Azores Islands, as well as the island of Madeira. Merchants then used these Atlantic outposts as debarkation points for subsequent journeys. From these strategic points, Portugal spread its empire down the western coast of Africa to the Congo, along the western coast of India, and eventually to Brazil on the eastern coast of South America. It also established trading posts in China and Japan. While the Portuguese didn’t rule over an immense landmass, their strategic holdings of islands and coastal ports gave them almost unrivaled control of nautical trade routes and a global empire of trading posts during the 1400s.
The travels of Portuguese traders to western Africa introduced them to the African slave trade, already brisk among African states. Seeing the value of this source of labor in growing the profitable crop of sugar on their Atlantic islands, the Portuguese soon began exporting enslaved Africans along with African ivory and gold. Sugar fueled the Atlantic slave trade, and the Portuguese islands quickly became home to sugar plantations. The Portuguese also traded these enslaved people, introducing much-needed human capital to other European nations. In the following years, as European exploration spread, slavery spread as well. In time, much of the Atlantic World would become a gargantuan sugar-plantation complex in which Africans labored to produce the highly profitable commodity for European consumers.
AMERICANA
Elmina Castle
In 1482, Portuguese traders built Elmina Castle (also called São Jorge da Mina, or Saint George’s of the Mine) in present-day Ghana, on the west coast of Africa (Figure 2.3). A fortified trading post, it had mounted cannons facing out to sea, not inland toward continental Africa; the Portuguese had greater fear of a naval attack from other Europeans than of a land attack from Africans. Portuguese traders soon began to settle around the fort and established the town of Elmina.
SPANISH EXPLORATION AND CONQUEST
The Spanish established the first European settlements in the Americas, beginning in the Caribbean and extending throughout Central and South America by 1600. Thousands of Spaniards flocked to the Americas seeking wealth and status. The most famous of these Spanish adventurers are Christopher Columbus (who, though Italian himself, explored on behalf of the Spanish monarchs), Hernán Cortés, and Francisco Pizarro.
The history of Spanish exploration begins with the history of Spain itself. During the fifteenth century, Spain hoped to gain advantage over its rival, Portugal. The marriage of Ferdinand of Aragon and Isabella of Castile in 1469 unified Catholic Spain and began the process of building a nation that could compete for worldwide power. Since the 700s, much of Spain had been under Islamic rule, and King Ferdinand II and Queen Isabella I, arch-defenders of the Catholic Church against Islam, were determined to defeat the Muslims in Granada, the last Islamic stronghold in Spain. In 1492, they completed the Reconquista: the centuries-long Christian conquest of the Iberian Peninsula. The Reconquista marked another step forward in the process of making Spain an imperial power, and Ferdinand and Isabella were now ready to look further afield.
Their goals were to expand Catholicism and to gain a commercial advantage over Portugal. To those ends, Ferdinand and Isabella sponsored extensive Atlantic exploration. Spain’s most famous explorer, Christopher Columbus, was actually from Genoa, Italy. He believed that, using calculations based on other mariners’ journeys, he could chart a westward route to India, which could be used to expand European trade and spread Christianity. Starting in 1485, he approached Genoese, Venetian, Portuguese, English, and Spanish monarchs, asking for ships and funding to explore this westward route. All those he petitioned—including Ferdinand and Isabella at first—rebuffed him; their nautical experts all concurred that Columbus’s estimates of the width of the Atlantic Ocean were far too low. However, after three years of entreaties, and, more important, the completion of the Reconquista, Ferdinand and Isabella agreed to finance Columbus’s expedition in 1492, supplying him with three ships: the Nina, the Pinta, and the Santa Maria. The Spanish monarchs knew that Portuguese mariners had reached the southern tip of Africa and sailed the Indian Ocean. They understood that the Portuguese would soon reach Asia and, in this competitive race to reach the Far East, the Spanish rulers decided to act.
Columbus held erroneous views that shaped his thinking about what he would encounter as he sailed west. He believed the earth to be much smaller than its actual size and, since he did not know of the existence of the Americas, he fully expected to land in Asia. On October 12, 1492, however, he made landfall on an island in the Bahamas. He then sailed to an island he named Hispaniola (present-day Dominican Republic and Haiti) (Figure 2.4). Believing he had landed in the East Indies, Columbus called the native Taínos he found there “Indios,” giving rise to the term “Indian” for any native people of the New World. Upon Columbus’s return to Spain, the Spanish crown bestowed on him the title of Admiral of the Ocean Sea and named him governor and viceroy of the lands he had discovered. As a devoted Catholic, Columbus had agreed with Ferdinand and Isabella prior to sailing west that part of the expected wealth from his voyage would be used to continue the fight against Islam.
Columbus’s 1493 letter—or probanza de mérito (proof of merit)—describing his “discovery” of a New World did much to inspire excitement in Europe. Probanzas de méritos were reports and letters written by Spaniards in the New World to the Spanish crown, designed to win royal patronage. Today they highlight the difficult task of historical work; while the letters are primary sources, historians need to understand the context and the culture in which the conquistadors, as the Spanish adventurers came to be called, wrote them and distinguish their bias and subjective nature. While they are filled with distortions and fabrications, probanzas de méritos are still useful in illustrating the expectation of wealth among the explorers as well as their view that native peoples would not pose a serious obstacle to colonization.
In 1493, Columbus sent two copies of a probanza de mérito to the Spanish king and queen and their minister of finance, Luis de Santángel. Santángel had supported Columbus’s voyage, helping him to obtain funding from Ferdinand and Isabella. Copies of the letter were soon circulating all over Europe, spreading news of the wondrous new land that Columbus had “discovered.” Columbus would make three more voyages over the next decade, establishing Spain’s first settlement in the New World on the island of Hispaniola. Many other Europeans followed in Columbus’s footsteps, drawn by dreams of winning wealth by sailing west. Another Italian, Amerigo Vespucci, sailing for the Portuguese crown, explored the South American coastline between 1499 and 1502. Unlike Columbus, he realized that the Americas were not part of Asia but lands unknown to Europeans. Vespucci’s widely published accounts of his voyages fueled speculation and intense interest in the New World among Europeans. Among those who read Vespucci’s reports was the German mapmaker Martin Waldseemüller. Using the explorer’s first name as a label for the new landmass, Waldseemüller attached “America” to his map of the New World in 1507, and the name stuck.
DEFINING AMERICAN
Columbus’s Probanza de mérito of 1493
The exploits of the most famous Spanish explorers have provided Western civilization with a narrative of European supremacy and Native American savagery. However, these stories are based on the self-aggrandizing efforts of conquistadors to secure royal favor through the writing of probanzas de méritos (proofs of merit). Below are excerpts from Columbus’s 1493 letter to Luis de Santángel, which illustrates how fantastic reports from European explorers gave rise to many myths surrounding the Spanish conquest and the New World.
This island, like all the others, is most extensive. It has many ports along the sea-coast excelling any in Christendom—and many fine, large, flowing rivers. The land there is elevated, with many mountains and peaks incomparably higher than in the centre isle. They are most beautiful, of a thousand varied forms, accessible, and full of trees of endless varieties, so high that they seem to touch the sky, and I have been told that they never lose their foliage. . . . There is honey, and there are many kinds of birds, and a great variety of fruits. Inland there are numerous mines of metals and innumerable people. Hispaniola is a marvel. Its hills and mountains, fine plains and open country, are rich and fertile for planting and for pasturage, and for building towns and villages. The seaports there are incredibly fine, as also the magnificent rivers, most of which bear gold. The trees, fruits and grasses differ widely from those in Juana. There are many spices and vast mines of gold and other metals in this island. They have no iron, nor steel, nor weapons, nor are they fit for them, because although they are well-made men of commanding stature, they appear extraordinarily timid. The only arms they have are sticks of cane, cut when in seed, with a sharpened stick at the end, and they are afraid to use these. Often I have sent two or three men ashore to some town to converse with them, and the natives came out in great numbers, and as soon as they saw our men arrive, fled without a moment’s delay although I protected them from all injury.
What does this letter show us about Spanish objectives in the New World? How do you think it might have influenced Europeans reading about the New World for the first time?
The 1492 Columbus landfall accelerated the rivalry between Spain and Portugal, and the two powers vied for domination through the acquisition of new lands. In the 1480s, Pope Sixtus IV had granted Portugal the right to all land south of the Cape Verde islands, leading the Portuguese king to claim that the lands discovered by Columbus belonged to Portugal, not Spain. Seeking to ensure that Columbus’s finds would remain Spanish, Spain’s monarchs turned to the Spanish-born Pope Alexander VI, who issued two papal decrees in 1493 that gave legitimacy to Spain’s Atlantic claims at the expense of Portugal. Hoping to salvage Portugal’s Atlantic holdings, King João II began negotiations with Spain. The resulting Treaty of Tordesillas in 1494 drew a north-to-south line through South America (Figure 2.5); Spain gained territory west of the line, while Portugal retained the lands east of the line, including the east coast of Brazil.
Columbus’s discovery opened a floodgate of Spanish exploration. Inspired by tales of rivers of gold and timid, malleable natives, later Spanish explorers were relentless in their quest for land and gold. Hernán Cortés hoped to gain hereditary privilege for his family, tribute payments and labor from natives, and an annual pension for his service to the crown. Cortés arrived on Hispaniola in 1504 and took part in the conquest of that island. In anticipation of winning his own honor and riches, Cortés later explored the Yucatán Peninsula. In 1519, he entered Tenochtitlán, the capital of the Aztec (Mexica) Empire. He and his men were astonished by the incredibly sophisticated causeways, gardens, and temples in the city, but they were horrified by the practice of human sacrifice that was part of the Aztec religion. Above all else, the Aztec wealth in gold fascinated the Spanish adventurers.
Hoping to gain power over the city, Cortés took Moctezuma, the Aztec ruler, hostage. The Spanish then murdered hundreds of high-ranking Mexica during a festival to celebrate Huitzilopochtli, the god of war. This angered the people of Tenochtitlán, who rose up against the interlopers in their city. Cortés and his people fled for their lives, running down one of Tenochtitlán’s causeways to safety on the shore. Smarting from their defeat at the hands of the Aztec, Cortés slowly created alliances with native peoples who resented Aztec rule. It took nearly a year for the Spanish and the tens of thousands of native allies who joined them to defeat the Mexica in Tenochtitlán, which they did by laying siege to the city. Only by playing upon the disunity among the diverse groups in the Aztec Empire were the Spanish able to capture the grand city of Tenochtitlán. In August 1521, having successfully fomented civil war as well as fended off rival Spanish explorers, Cortés claimed Tenochtitlán for Spain and renamed it Mexico City.
The traditional European narrative of exploration presents the victory of the Spanish over the Aztec as an example of the superiority of the Europeans over the “savage Indians.” However, the reality is far more complex. When Cortés explored central Mexico, he encountered a region simmering with conflict. Far from being unified and content under Aztec rule, many peoples in Mexico resented it and were ready to rebel. One group in particular, the Tlaxcalan, threw their lot in with the Spanish, providing as many as 200,000 fighters in the siege of Tenochtitlán. The Spanish also brought smallpox into the valley of Mexico. The disease took a heavy toll on the people in Tenochtitlán, playing a much greater role in the city’s demise than did the Spanish force of arms.
Cortés was also aided by a Nahua woman called Malintzin (also known as La Malinche or Doña Marina, her Spanish name), whom the natives of Tabasco gave him as tribute. Malintzin translated for Cortés in his dealings with Moctezuma and, whether willingly or under pressure, entered into a physical relationship with him. Their son, Martín, may have been the first mestizo (person of mixed indigenous American and European descent). Malintzin remains a controversial figure in the history of the Atlantic World; some people view her as a traitor because she helped Cortés conquer the Aztecs, while others see her as a victim of European expansion. In either case, she demonstrates one way in which native peoples responded to the arrival of the Spanish. Without her, Cortés would not have been able to communicate, and without the language bridge, he surely would have been less successful in destabilizing the Aztec Empire. By this and other means, native people helped shape the conquest of the Americas.
Spain’s acquisitiveness seemingly knew no bounds as groups of its explorers searched for the next trove of instant riches. One such explorer, Francisco Pizarro, made his way to the Spanish Caribbean in 1509, drawn by the promise of wealth and titles. He participated in successful expeditions in Panama before following rumors of Inca wealth to the south. Although his first efforts against the Inca Empire in the 1520s failed, Pizarro captured the Inca emperor Atahualpa in 1532 and executed him one year later. In 1533, Pizarro founded Lima, Peru. Like Cortés, Pizarro had to combat not only the natives of the new worlds he was conquering but also competitors from his own country; a Spanish rival assassinated him in 1541.
Spain’s drive to enlarge its empire led other hopeful conquistadors to push further into the Americas, hoping to replicate the success of Cortés and Pizarro. Hernando de Soto had participated in Pizarro’s conquest of the Inca, and from 1539 to 1542 he led expeditions to what is today the southeastern United States, looking for gold. He and his followers explored what is now Florida, Georgia, the Carolinas, Tennessee, Alabama, Mississippi, Arkansas, Oklahoma, Louisiana, and Texas. Everywhere they traveled, they brought European diseases, which claimed thousands of native lives as well as the lives of the explorers. In 1542, de Soto himself died during the expedition. The surviving Spaniards, numbering a little over three hundred, returned to Mexico City without finding the much-anticipated mountains of gold and silver.
Francisco Vásquez de Coronado was born into a noble family and went to Mexico, then called New Spain, in 1535. He presided as governor over the province of Nueva Galicia, where he heard rumors of wealth to the north: a golden city called Quivira. Between 1540 and 1542, Coronado led a large expedition of Spaniards and native allies to the lands north of Mexico City, and for the next several years, they explored the area that is now the southwestern United States (Figure 2.6). During the winter of 1540–41, the explorers waged war against the Tiwa in present-day New Mexico. Rather than leading to the discovery of gold and silver, however, the expedition simply left Coronado bankrupt.
Gumbo
Spain’s Missed Opportunity in Louisiana:
As noted above, Spain hoped to follow up the success of Cortés and Pizarro in Central and South America by sending out explorers to North America. Few made it into what we would now consider Louisiana, but of the early ones who did, Hernando de Soto was the most important. In 1539, he and 600 men landed in Florida and traveled through much of the modern southeastern United States including parts of Louisiana on a three-year journey. In Natchez, de Soto came upon the Mississippi River and was the first European to document its existence. He died shortly after, but his men eventually sailed down through the mouth of the river into the Gulf of Mexico in 1543.
These men left behind a detailed description of much of the landscape of the region, but the lack of references to anything of great value led Spain to turn their attention elsewhere for decades. As a result, Spain would not be the first to attempt long-term settlement in Louisiana. That would be left up to one of their rivals, France.
This information can be found on pages 24-26 of the following book: Wall, Bennett H., and John C. Rodrigue. Louisiana: A History. 6th ed., Wiley, 2013.
THE SPANISH GOLDEN AGE
The exploits of European explorers had a profound impact both in the Americas and back in Europe. An exchange of ideas, fueled and financed in part by New World commodities, began to connect European nations and, in turn, to touch the parts of the world that Europeans conquered. In Spain, gold and silver from the Americas helped to fuel a golden age, the Siglo de Oro, when Spanish art and literature flourished. Riches poured in from the colonies, and new ideas poured in from other countries and new lands. The Hapsburg dynasty, which ruled a collection of territories including Austria, the Netherlands, Naples, Sicily, and Spain, encouraged and financed the work of painters, sculptors, musicians, architects, and writers, resulting in the blooming of Spanish Renaissance culture. One of this period’s most famous works is the novel The Ingenious Gentleman Don Quixote of La Mancha by Miguel de Cervantes. This two-volume book (1605 and 1618) told a colorful tale of a hidalgo (gentleman) who reads so many tales of chivalry and knighthood that he becomes unable to tell reality from fiction. With his faithful sidekick Sancho Panza, Don Quixote leaves reality behind and sets out to revive chivalry by doing battle with what he perceives as the enemies of Spain.
CLICK AND EXPLORE
Explore the collection at The Cervantes Project for images, complete texts, and other resources relating to Cervantes’s works.
Spain attracted innovative foreign painters such as El Greco, a Greek who had studied with Italian Renaissance masters like Titian and Michelangelo before moving to Toledo. Native Spaniards created equally enduring works. Las Meninas (The Maids of Honor), painted by Diego Velázquez in 1656, is one of the best-known paintings in history. Velázquez painted himself into this imposingly large royal portrait (he’s shown holding his brush and easel on the left) and boldly placed the viewer where the king and queen would stand in the scene (Figure 2.7).


161 Putting It Together: Teamwork and Communication
Summary
In this module you learned about the importance of teamwork and communication in business. Below is a summary of the key points that were covered.
Groups and Teams
Teams are groups of individuals with complementary skills who come together to achieve a specific goal. Teams can be manager-led, self-directed, cross-functional, or even virtual. Companies use teams because they are an effective means of achieving objectives, and they bring increased efficiency to operations.
Team Development
When teams are formed they evolve from individuals into a cohesive unit. The stages of team development are: forming, storming, norming, and performing.
Team Success
What differentiates a successful team from an unsuccessful one? Some of the hallmarks of successful teams are the following: the members trust one another, the members become “boosters” for one another, members enjoy the team activities, and leadership is shared.
Effective Communication
Effective communications are based on empathy, and they are thoughtful, clear, specific, brief, and timely. Effective communicators are aware that only a portion of their message is verbally conveyed, so they are careful about tone, diction, and body language. Finally, in order to communicate effectively one must be an active and engaged listener.
Appropriate Communication in Business
Knowing how to appropriately communicate in a business setting has been complicated by the introduction and use of mobile technology and social media. In addition, some workplaces have adopted a more casual dress code, making it appear that casual communication methods are appropriate. Understanding when and how each form of communication should be used depends on the sender, receiver, and message involved.
Communication Flow
Communications flow like a river through a variety of channels, both formal and informal. In addition, communication channels are both external and internal to the organization. Each channel has advantages and disadvantages and must be managed in order to ensure that the appropriate message is being conveyed to the appropriate parties.
Barriers to Communication
“Getting one’s message across” can be tricky and challenging due to barriers that impede communication. Among the barriers to effective communication are filtering, selective perspective, information overload, lack of source credibility, emotional disconnects, semantics, gender differences, and poor listening skills.
Synthesis
What did it take for these eight people to jump out of a perfectly good airplane and join hands to form a figure eight? Yes, nerves of steel and a measure of pure insanity. But it also took something else—the very thing you learned about in this module: teamwork and communication. As for these skydivers, the consequences of poor teamwork and faulty communication can be serious and even deadly. Defective parts can wind up in automobiles and airplanes, the wrong medications can be given to patients in a hospital, food can be contaminated . . . all as a result of poor teamwork and communication. Understanding the ways in which people communicate and learning to overcome potential barriers can help you be a more effective communicator and a better team member. Moreover, the skills you’ve learned in this module are not only important in business—they’re useful in skydiving and life.


3.1 How Cells Are Studied
Learning Objectives
By the end of this section, you will be able to:
- Describe the roles of cells in organisms
- Compare and contrast light microscopy and electron microscopy
- Summarize the cell theory
Watch a video about eukaryotic cells
Watch a video about diffusion
A cell is the smallest unit of a living thing. A living thing, like you, is called an organism.
In multicellular organisms, several cells of one particular kind interconnect with each other and perform shared functions to form tissues (for example, muscle tissue, connective tissue, and nervous tissue), several tissues combine to form an organ (for example, stomach, heart, or brain), and several organs make up an organ system (such as the digestive system, circulatory system, or nervous system). Several systems functioning together form an organism (such as an elephant, for example).
There are many types of cells, and all are grouped into one of two broad categories: prokaryotic and eukaryotic. Animal cells, plant cells, fungal cells, and protist cells are classified as eukaryotic, whereas bacteria and archaea cells are classified as prokaryotic. Before discussing the criteria for determining whether a cell is prokaryotic or eukaryotic, let us first examine how biologists study cells.
Microscopy
Cells vary in size.  A microscope is an instrument that magnifies an object. Most images of cells are taken with a microscope and are called micrographs.
Light Microscopes
To give you a sense of the size of a cell, a typical human red blood cell is about eight millionths of a meter or eight micrometers (abbreviated as µm) in diameter; the head of a pin is about two thousandths of a meter (millimeters, or mm) in diameter. That means that approximately 250 red blood cells could fit on the head of a pin.
The optics of the lenses of a light microscope changes the orientation of the image. A specimen that is right-side up and facing right on the microscope slide will appear upside-down and facing left when viewed through a microscope, and vice versa. Similarly, if the slide is moved left while looking through the microscope, it will appear to move right, and if moved down, it will seem to move up. This occurs because microscopes use two sets of lenses to magnify the image. Due to the manner in which light travels through the lenses, this system of lenses produces an inverted image (binoculars and a dissecting microscope work in a similar manner, but include an additional magnification system that makes the final image appear to be upright).
Most student microscopes are classified as light microscopes (Figure 3.2 a). Visible light both passes through and is bent by the lens system to enable the user to see the specimen. Light microscopes are advantageous for viewing living organisms, but since individual cells are generally transparent, their components are not distinguishable unless they are colored with special stains. Staining, however, usually kills the cells.
Light microscopes commonly used in the undergraduate college laboratory magnify up to approximately 400 times. Two parameters that are important in microscopy are magnification and resolving power. Magnification is the degree of enlargement of an object. Resolving power is the ability of a microscope to allow the eye to distinguish two adjacent structures as separate; the higher the resolution, the closer those two objects can be, and the better the clarity and detail of the image. When oil immersion lenses are used, magnification is usually increased to 1,000 times for the study of smaller cells, like most prokaryotic cells. Because light entering a specimen from below is focused onto the eye of an observer, the specimen can be viewed using light microscopy. For this reason, for light to pass through a specimen, the sample must be thin or translucent.
A second type of microscope used in laboratories is the dissecting microscope (Figure 3.2 b). These microscopes have a lower magnification (20 to 80 times the object size) than light microscopes and can provide a three-dimensional view of the specimen. Thick objects can be examined with many components in focus at the same time. These microscopes are designed to give a magnified and clear view of tissue structure as well as the anatomy of the whole organism. Like light microscopes, most modern dissecting microscopes are also binocular, meaning that they have two separate lens systems, one for each eye. The lens systems are separated by a certain distance, and therefore provide a sense of depth in the view of their subject to make manipulations by hand easier. Dissecting microscopes also have optics that correct the image so that it appears as if being seen by the naked eye and not as an inverted image. The light illuminating a sample under a dissecting microscope typically comes from above the sample, but may also be directed from below.
Electron Microscopes
In contrast to light microscopes, electron microscopes use a beam of electrons instead of a beam of light. Not only does this allow for higher magnification and, thus, more detail (Figure 3.4), it also provides higher resolving power. Preparation of a specimen for viewing under an electron microscope will kill it; therefore, live cells cannot be viewed using this type of microscopy. In addition, the electron beam moves best in a vacuum, making it impossible to view living materials.
In a scanning electron microscope, a beam of electrons moves back and forth across a cell’s surface, rendering the details of cell surface characteristics by reflection. Cells and other structures are usually coated with a metal like gold. In a transmission electron microscope, the electron beam is transmitted through the cell and provides details of a cell’s internal structures. As you might imagine, electron microscopes are significantly more bulky and expensive than are light microscopes.
Cytotechnologist: Have you ever heard of a medical test called a Pap smear? In this test, a doctor takes a small sample of cells from the uterine cervix of a patient and sends it to a medical lab where a cytotechnologist stains the cells and examines them for any changes that could indicate cervical cancer or a microbial infection.
Cytotechnologists (cyto– = cell) are professionals who study cells through microscopic examinations and other laboratory tests. They are trained to determine which cellular changes are within normal limits or are abnormal. Their focus is not limited to cervical cells; they study cellular specimens that come from all organs. When they notice abnormalities, they consult a pathologist, who is a medical doctor who can make a clinical diagnosis.
Cytotechnologists play vital roles in saving people’s lives. When abnormalities are discovered early, a patient’s treatment can begin sooner, which usually increases the chances of successful treatment.
Cell Theory
The microscopes we use today are far more complex than those used in the 1600s by Antony van Leeuwenhoek, a Dutch shopkeeper who had great skill in crafting lenses. Despite the limitations of his now-ancient lenses, van Leeuwenhoek observed the movements of protists (a type of single-celled organism) and sperm, which he collectively termed “animalcules.”
In a 1665 publication called Micrographia, experimental scientist Robert Hooke coined the term “cell” (from the Latin cella, meaning “small room”) for the box-like structures he observed when viewing cork tissue through a lens. In the 1670s, van Leeuwenhoek discovered bacteria and protozoa. Later advances in lenses and microscope construction enabled other scientists to see different components inside cells.
By the late 1830s, botanist Matthias Schleiden and zoologist Theodor Schwann were studying tissues and proposed the unified cell theory, which states that all living things are composed of one or more cells, that the cell is the basic unit of life, and that all new cells arise from existing cells. These principles still stand today.
Section Summary
A cell is the smallest unit of life. Most cells are so small that they cannot be viewed with the naked eye. Therefore, scientists must use microscopes to study cells. Electron microscopes provide higher magnification, higher resolution, and more detail than light microscopes. The unified cell theory states that all organisms are composed of one or more cells, the cell is the basic unit of life, and new cells arise from existing cells.
Exercises
Glossary
microscope: the instrument that magnifies an object
unified cell theory: the biological concept that states that all organisms are composed of one or more cells, the cell is the basic unit of life, and new cells arise from existing cells
Media Attributions
- Figure 3.2
- Figure 3.3 © Modification of work by CDC, Armed Forces Institute of Pathology, Charles N. Farmer is licensed under a Public Domain license
- Figure 3.4 © Modification of work by Rocky Mountain Laboratories, NIAID, NIH; scale-bar data from Matt Russell
- Figure 3.5 © Modification of work by Ed Uthman; Scale-bar data from Matt Russell is licensed under a CC BY-SA (Attribution ShareAlike) license


10.18 Tailstock Cutting Operations
Micky R. Jennings
What are they?
Drilling, reaming, tapping, countersinking, and counterboring are the main tailstock cutting operations performed on a lathe. Tailstock cutting operations are basically the same hole making operations that could be performed in a drill press, except they are performed horizontally and in the center of a rotating workpiece. One key advantage of performing these operations on a lathe is that no layout line is needed and there is no center punch mark to chase around. The hole can easily be made in line with the center of the spindle.
Step by step process for tailstock drilling:
- Clean the Morse taper of the tailstock.
- Clean the Morse taper shank of a drill chuck
- Install the drill chuck into the tailstock by quickly and forcefully inserting the tool into the taper of the tailstock.
- Install a center drill or spot drill into the drill chuck.
- Calculate and select a spindle speed appropriate for spotting the hole.
- Turn on the spindle.
- Apply a drop of oil to the tip of the tool.
- Spot the hole.
- Remove the spotting tool, drill chuck, and install the twist drill.
- Calculate and select a spindle speed appropriate for drilling the hole.
- Oil drill.
- The depth of a hole drilled on a lathe can be determined by a semi-precision method using the graduations on the quill or a more precise method using the graduations on the hand wheel.
- Drill the hole in a similar fashion to that of a drill press. The lathe is often much more powerful than the drill press; therefore, it can perform heavier machining operations and use larger twist drills without the need for pilot drilling.
- Remove the twist drill and install whatever secondary operation may be required.
- Calculate and select the spindle speed, then perform the operation in the same fashion as on a drill press.
“Step 8: Spot the hole.”
“Step 9: Remove the spotting tool, drill chuck, and install the twist drill.”
“Step 11: Oil drill.”
“Step 13: Drill the hole in a similar fashion to that of a drill press. The lathe is often much more powerful than the drill press; therefore, it can perform heavier machining operations and use larger twist drills without the need for pilot drilling.”
Attributions
- Figure 10.216: Tailstock Drilling by Micky R. Jennings, courtesy of Wenatchee Valley College, for WA Open ProfTech, © SBCTC, CC BY 4.0
- Video 10.104: Micky R. Jennings, courtesy of Wenatchee Valley College, for WA Open ProfTech, © SBCTC, CC BY 4.0
- Figure 10.217: Installing a Taper Shank Drill by Micky R. Jennings, courtesy of Wenatchee Valley College, for WA Open ProfTech, © SBCTC, CC BY 4.0
- Video 10.105: Micky R. Jennings, courtesy of Wenatchee Valley College, for WA Open ProfTech, © SBCTC, CC BY 4.0
- Video 10.106: Micky R. Jennings, courtesy of Wenatchee Valley College, for WA Open ProfTech, © SBCTC, CC BY 4.0


4 Outcome: What Is Economics?
What you’ll learn to do: explain what economics is and explain why it is important
In order to understand economics it’s important to master a set of key definitions and understand how they interconnect. These concepts will be used many times throughout the course. At the most basic level:
- Scarcity means that there are never enough resources to satisfy all human wants
- Economics is the study of the trade-offs and choices that we make, given the fact of scarcity
- Opportunity cost is what we give up when we choose one thing over another
We will spend more time with these definitions, and understand how they’re used in the context of this discipline.
The specific things you’ll learn in this section include the following:
- Define scarcity and explain its economic impact
- Define opportunity cost
- Define productive resources
- Explain why trade and markets exist
- Distinguish between macroeconomics and microeconomics
Learning Activities
The learning activities for this section include the following:
- Video: Scarcity and Choice
- Reading: Understanding Economics and Scarcity
- Video: Resources
- Reading: The Concept of Opportunity Cost
- Video: Opportunity Cost
- Reading: Labor, Markets, and Trade
- Reading: Microeconomics and Macroeconomics


88 Google Scholar
An increasingly popular article database is Google Scholar. It looks like a regular Google search, and it aims to include the vast majority of scholarly resources available. While it has some limitations (like not including a list of which journals they include), it’s a very useful tool if you want to cast a wide net.
Here are three tips for using Google Scholar effectively:
- Add your topic field (economics, psychology, French, etc.) as one of your keywords. If you just put in “crime,” for example, Google Scholar will return all sorts of stuff from sociology, psychology, geography, and history. If your paper is on crime in French literature, your best sources may be buried under thousands of papers from other disciplines. A set of search terms like “crime French literature modern” will get you to relevant sources much faster.
- Don’t ever pay for an article. When you click on links to articles in Google Scholar, you may end up on a publisher’s site that tells you that you can download the article for $20 or $30. Don’t do it! You probably have access to virtually all the published academic literature through your library resources. Write down the key information (authors’ names, title, journal title, volume, issue number, year, page numbers) and go find the article through your library website. If you don’t have immediate full-text access, you may be able to get it through inter-library loan.
- Use the “cited by” feature. If you get one great hit on Google Scholar, you can quickly see a list of other papers that cited it. For example, the search terms “crime economics” yielded this hit for a 1988 paper that appeared in a journal called Kyklos:
Using Google Scholar
Watch this video to get a better idea of how to utilize Google Scholar for finding articles. While this video shows specifics for setting up an account with Eastern Michigan University, the same principles apply to other colleges and universities. Ask your librarian if you have more questions.


1.2 Why Study Earth?
The simple answer to this question is that Earth is our home — our only home for the foreseeable future — and in order to ensure that it continues to be a great place to live, we need to understand how it works. Another answer is that some of us can’t help but study it because it’s fascinating. But there is more to it than that:
- We rely on Earth for valuable resources such as soil, water, metals, industrial minerals, and energy, and we need to know how to find these resources and exploit them sustainably.
- We can study rocks and the fossils they contain to understand the evolution of our environment and the life within it.
- We can learn to minimize our risks from earthquakes, volcanoes, slope failures, and damaging storms.
- We can learn how and why Earth’s climate has changed in the past, and use that knowledge to understand both natural and human-caused climate change.
- We can recognize how our activities have altered the environment in many ways and the climate in increasingly serious ways, and how to avoid more severe changes in the future.
- We can use our knowledge of Earth to understand other planets in our solar system, as well as those around distant stars.
An example of the importance of geological studies for minimizing risks to the public is illustrated in Figure 1.2. This is a slope failure that took place in January 2005 in the Riverside Drive area of North Vancouver. The steep bank beneath the house shown gave way, and a slurry of mud and sand flowed down, destroying another house below and killing one person. This event took place following a heavy rainfall, which is a common occurrence in southwestern B.C. in the winter.
The irony of the 2005 slope failure is that the District of North Vancouver had been warned in a geological report written in 1980 that this area was prone to slope failure and that steps should be taken to minimize the risk to residents. Very little was done in the intervening 25 years, and the results were deadly.


Chapter 30: Political Storms at Home and Abroad, 1968-1980
Vietnam: The Downward Spiral
Learning Objectives
By the end of this section, you will be able to:
- Describe the events that fueled antiwar sentiment in the Vietnam era
- Explain Nixon’s steps to withdraw the United States from the conflict in South Vietnam
As early as 1967, critics of the war in Vietnam had begun to call for the repeal of the Gulf of Tonkin Resolution, which gave President Johnson the authority to conduct military operations in Vietnam in defense of an ally, South Vietnam. Nixon initially opposed the repeal efforts, claiming that doing so might have consequences that reached far beyond Vietnam. Nevertheless, by 1969, he was beginning troop withdrawals from Vietnam while simultaneously looking for a “knockout blow” against the North Vietnamese. In sum, the Nixon administration was in need of an exit strategy.
The escalation of the war, however, made an easy withdrawal increasingly difficult. Officially, the United States was the ally and partner of the South Vietnamese, whose “hearts and minds” it was trying to win through a combination of military assistance and economic development. In reality, however, U.S. soldiers, who found themselves fighting in an inhospitable environment thousands of miles from home to protect people who often resented their presence and aided their enemies, came to regard the Vietnamese as backward, cowardly people land the government of South Vietnam as hopelessly inefficient and corrupt. Instead of winning “hearts and minds,” U.S. warfare in Vietnam cost the lives and limbs of U.S. troops and millions of Vietnamese combatants and civilians
For their part, the North Vietnamese forces and the National Liberation Front in South Vietnam also used brutal tactics to terrorize and kill their opponents or effectively control their territory. Political assassinations and forced indoctrination were common. Captured U.S. soldiers frequently endured torture and imprisonment.
MY LAI
Racism on the part of some U.S. soldiers and a desire to retaliate against those they perceived to be responsible for harming U.S. troops affected the conduct of the war. A war correspondent who served in Vietnam noted, “In motivating the GI to fight by appealing to his racist feelings, the United States military discovered that it had liberated an emotion over which it was to lose control.” It was not unusual for U.S. soldiers to evacuate and burn villages suspected of shielding Viet Cong fighters, both to deprive the enemy of potential support and to enact revenge for enemy brutality. Troops shot at farmers’ water buffalo for target practice. American and South Vietnamese use of napalm, a jellied gasoline that sticks to the objects it burns, was common. Originally developed to burn down structures during World War II, in Vietnam, it was directed against human beings as well, as had occurred during the Korean War.
Vietnam Veterans against the War Statement
Many U.S. soldiers disapproved of the actions of their fellow troops. Indeed, a group of Vietnam veterans formed the organization Vietnam Veterans Against the War (WAW). Small at first, it grew to perhaps as many as twenty thousand members. In April 1971, John Kerry, a former lieutenant in the U.S. Navy and a member of WAW, testified before the U.S. Senate Committee on Foreign Relations about conditions in Vietnam based on his personal observations:
“I would like to talk on behalf of all those veterans and say that several months ago in Detroit we had an investigation at which over 150 honorably discharged, and many very highly decorated, veterans testified to war crimes committed in Southeast Asia. These were not isolated incidents but crimes committed on a day-to-day basis with the full awareness of officers at all levels of command…. They relived the absolute horror of what this country, in a sense, made them do.
They told stories that at times they had personally raped, cut off ears, cut off heads … randomly shot at civilians, razed villages … and generally ravaged the countryside of South Vietnam in addition to the normal ravage of war and the normal and very particular ravaging which is done by the applied bombing power of this country….
We could come back to this country, we could be quiet, we could hold our silence, we could not tell what went on in Vietnam, but we feel because of what threatens this country, not the reds [Communists], but the crimes which we are committing that threaten it, that we have to speak out.”
–John Kerry, April 23, 1971
In what way did the actions of U.S. soldiers in Vietnam threaten the United States?
On March 16, 1968, men from the U.S. Army’s Twenty-Third Infantry Division committed one of the most notorious atrocities of the war. About one hundred soldiers commanded by Captain Ernest Medina were sent to destroy the village of My Lai, which was suspected of hiding Viet Cong fighters. Although there was later disagreement regarding the captain’s exact words, the platoon leaders believed the order to destroy the enemy included killing women and children. Having suffered twenty-eight casualties in the past three months, the men of Charlie Company were under severe stress and extremely apprehensive as they approached the village. Two platoons entered it, shooting randomly. A group of seventy to eighty unarmed people, including children and infants, were forced into an irrigation ditch by members of the First Platoon under the command of Lt. William L. Calley, Jr. Despite their proclamations of innocence, the villagers were shot (Figure 30.13). Houses were set on fire, and as the inhabitants tried to flee, they were killed with rifles, machine guns, and grenades. The U.S. troops were never fired upon, and one soldier later testified that he did not see any man who looked like a Viet Cong fighter.
The precise number of civilians killed that day is unclear: The numbers range from 347 to 504. None were armed. Although not all the soldiers in My Lai took part in the killings, no one attempted to stop the massacre before the arrival by helicopter of Warrant Officer Hugh Thompson, who, along with his crew, attempted to evacuate women and children. Upon returning to his base, Thompson immediately reported the events taking place at My Lai. Shortly thereafter, Medina ordered Charlie Company to cease fire. Although Thompson’s crewmembers confirmed his account, none of the men from Charlie Company gave a report, and a cover-up began almost immediately. The army first claimed that 150 people, the majority of them Viet Cong, had been killed during a firefight with Charlie Company.
Hearing details from friends in Charlie Company, a helicopter gunner by the name of Ron Ridenhour began to conduct his own investigation and, in April 1969, wrote to thirty members of Congress, demanding an investigation. By September 1969, the army charged Lt. Calley with premeditated murder. Many Americans were horrified at the graphic footage of the massacre; the incident confirmed their belief that the war was unjust and not being fought on behalf of the Vietnamese people. However, nearly half of the respondents to a Minnesota poll did not believe that the incident at My Lai had actually happened. U.S. soldiers could not possibly do such horrible things, they felt; they were certain that American goals in Vietnam were honorable and speculated that the antiwar movement had concocted the story to generate sympathy for the enemy.
Calley was found guilty in March 1971, and sentenced to life in prison. Nationwide, hundreds of thousands of Americans joined a “Free Calley” campaign. Two days later, President Nixon released him from custody and placed him under him house arrest at Fort Benning, Georgia. In August of that same year, Calley’s sentence was reduced to twenty years, and in September 1974, he was paroled. The only soldier convicted in the massacre, he spent a total of three-and-a-half years under house arrest for his crimes.
BATTLES AT HOME
As the conflict wore on and reports of brutalities increased, the antiwar movement grew in strength. To take the political pressure off himself and his administration, and find a way to exit Vietnam “with honor,” Nixon began the process of Vietnamization, turning more responsibility for the war over to South Vietnamese forces by training them and providing American weaponry, while withdrawing U.S. troops from the field. At the same time, however, Nixon authorized the bombing of neighboring Cambodia, which had declared its neutrality, in an effort to destroy North Vietnamese and Viet Cong bases within that country and cut off supply routes between North and South Vietnam. The bombing was kept secret from both Congress and the American public. In April 1970, Nixon decided to follow up with an invasion of Cambodia.
The invasion could not be kept secret, and when Nixon announced it on television on April 30, 1970, protests sprang up across the country. The most tragic and politically damaging occurred on May 1, 1970, at Kent State University in Ohio. Violence erupted in the town of Kent after an initial student demonstration on campus, and the next day, the mayor asked Ohio’s governor to send in the National Guard. Troops were sent to the university’s campus, where students had set fire to the ROTC building and were fighting off firemen and policemen trying to extinguish it. The National Guard used teargas to break up the demonstration, and several students were arrested (Figure 30.14).
Tensions came to a head on May 4. Although campus officials had called off a planned demonstration, some fifteen hundred to two thousand students assembled, throwing rocks at a security officer who ordered them to leave. Seventy-seven members of the National Guard, with bayonets attached to their rifles, approached the students. After forcing most of them to retreat, the troops seemed to depart. Then, for reasons that are still unknown, they halted and turned; many began to fire at the students. Nine students were wounded; four were killed. Two of the dead had simply been crossing campus on their way to class. Peace was finally restored when a faculty member pleaded with the remaining students to leave.
Click and Explore
Read the New York Times account of the shootings at Kent State University and view (under the headline) one of the most iconic photographs in American history.
News of the Kent State shootings shocked students around the country. Millions refused to attend class, as strikes were held at hundreds of colleges and high schools across the United States. On May 8, an antiwar protest took place in New York City, and the next day, 100,000 protesters assembled in Washington, DC. Not everyone sympathized with the slain students, however. Nixon had earlier referred to student demonstrators as “bums,” and construction workers attacked the New York City protestors. A Gallup poll revealed that most Americans blamed the students for the tragic events at Kent State.
On May 15, a similar tragedy took place at Jackson State College, an African American college in Jackson, Mississippi. Once again, students gathered on campus to protest the invasion of Cambodia, setting fires and throwing rocks. The police arrived to disperse the protesters, who had gathered outside a women’s dormitory. Shortly after midnight, the police opened fire with shotguns. The dormitory windows shattered, showering people with broken glass. Twelve were wounded, and two young men, one a student at the college and the other a local high school student, were killed.
PULLING OUT OF THE QUAGMIRE
Ongoing protests, campus violence, and the expansion of the war into Cambodia deeply disillusioned Americans about their role in Vietnam. Understanding the nation’s mood, Nixon dropped his opposition to a repeal of the Gulf of Tonkin Resolution of 1964. In January 1971, he signed Congress’s revocation of the notorious blanket military authorization. Gallup polls taken in May of that year revealed that only 28 percent of the respondents supported the war; many felt it was not only a mistake but also immoral.
Just as influential as antiwar protests and campus violence in turning people against the war was the publication of documents the media dubbed the Pentagon Papers in June 1971. These were excerpts from a study prepared during the Johnson administration that revealed the true nature of the conflict in Vietnam. The public learned for the first time that the United States had been planning to oust Ngo Dinh Them from the South Vietnamese government, that Johnson meant to expand the U.S. role in Vietnam and bomb North Vietnam even as he stated publicly that he had no intentions of doing so, and that his administration had sought to deliberately provoke North Vietnamese attacks in order to justify escalating American involvement. Copies of the study had been given to the New York Times and other newspapers by Daniel Ellsberg, one of the military analysts who had contributed to it. To avoid setting a precedent by allowing the press to publish confidential documents, Nixon’s attorney general, John Mitchell, sought an injunction against the New York Times to prevent its publication of future articles based on the Pentagon Papers. The newspaper appealed. On June 30, 1971, the U.S. Supreme Court held that the government could not prevent the publication of the articles.
Realizing that he must end the war but reluctant to make it look as though the United States was admitting its failure to subdue a small Asian nation, Nixon began maneuvering to secure favorable peace terms from the North Vietnamese. Thanks to his diplomatic efforts in China and the Soviet Union, those two nations cautioned North Vietnam to use restraint. The loss of strong support by their patrons, together with intensive bombing of Hanoi and the mining of crucial North Vietnamese harbors by U.S. forces, made the North Vietnamese more willing to negotiate.
Nixon’s actions had also won him popular support at home. By the 1972 election, voters again favored his Vietnam policy by a ratio of two to one. On January 27, 1973, Secretary of State Henry Kissinger signed an accord with Le Duc Tho, the chief negotiator for the North Vietnamese, ending American participation in the war. The United States was given sixty days to withdraw its troops, and North Vietnam was allowed to keep its forces in places it currently occupied. This meant that over 100,000 northern soldiers would remain in the South–ideally situated to continue the war with South Vietnam. The United States left behind a small number of military advisors as well as equipment, and Congress continued to approve funds for South Vietnam, but considerably less than in earlier years. So the war continued, but it was clear the South could not hope to defeat the North.
As the end was nearing, the United States conducted several operations to evacuate children from the South. On the morning of April 29, 1975, as North Vietnamese and Viet Cong forces moved through the outskirts of Saigon, orders were given to evacuate Americans and South Vietnamese who had supported the United States. Unable to use the airport, helicopters ferried Americans and Vietnamese refugees who had fled to the American embassy to ships off the coast. North Vietnamese forces entered Saigon the next day, and the South surrendered.
The war had cost the lives of more than 1.5 million Vietnamese combatants and civilians, as well as over 58,000 U.S. troops. But the war had caused another, more intangible casualty: the loss of consensus, confidence, and a sense of moral high ground in the American political culture.


38 8.2 A Single Population Mean using the Student t Distribution
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Goset (1876–1937) of the Guinness brewery in Dublin, Ireland ran into this problem. His experiments with hops and barley produced very few samples. Just replacing σ with s did not produce accurate results when he tried to calculate a confidence interval. He realized that he could not use a normal distribution for the calculation; he found that the actual distribution depends on the sample size. This problem led him to “discover” what is called the Student’s t-distribution. The name comes from the fact that Gosset wrote under the pen name “Student.”
Up until the mid-1970s, some statisticians used the normal distribution approximation for large sample sizes and only used the Student’s t-distribution only for sample sizes of at most 30. With graphing calculators and computers, the practice now is to use the Student’s t-distribution whenever s is used as an estimate for σ.
If you draw a simple random sample of size n from a population that has an approximately a normal distribution with mean μ and unknown population standard deviation σ and calculate the t-score: [latex]\displaystyle{t}=\frac{{\overline{{x}}-\mu}}{{\frac{{s}}{\sqrt{{n}}}}}[/latex] is from its mean μ. For each sample size n, there is a different Student’s t-distribution.
The degrees of freedom, n – 1, come from the calculation of the sample standard deviation s. Because the sum of the deviations is zero, we can find the last deviation once we know the other n – 1 deviations. The other n – 1 deviations can change or vary freely. We call the number n – 1 the degrees of freedom (df).
Properties of the Student’s t-Distribution
- The graph for the Student’s t-distribution is similar to the standard normal curve.
- The mean for the Student’s t-distribution is zero and the distribution is symmetric about zero.
- The Student’s t-distribution has more probability in its tails than the standard normal distribution because the spread of the t-distribution is greater than the spread of the standard normal. So the graph of the Student’s t-distribution will be thicker in the tails and shorter in the center than the graph of the standard normal distribution.
- The exact shape of the Student’s t-distribution depends on the degrees of freedom. As the degrees of freedom increases, the graph of Student’s t-distribution becomes more like the graph of the standard normal distribution.
- The underlying population of individual observations is assumed to be normally distributed with unknown population mean μ and unknown population standard deviation σ. The size of the underlying population is generally not relevant unless it is very small. If it is bell shaped (normal) then the assumption is met and doesn’t need discussion. Random sampling is assumed, but that is a completely separate assumption from normality.
Calculators and computers can easily calculate any Student’s t-probabilities. The TI-83,83+, and 84+ have a tcdf function to find the probability for given values of t. The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom).
However for confidence intervals, we need to use inverse probability to find the value of t when we know the probability.
For the TI-84+ you can use the invT command on the DISTRibution menu.
The invT command requires two inputs: invT(area to the left, degrees of freedom)
The output is the t-score that corresponds to the area we specified.
The TI-83 and 83+ do not have the invT command. (The TI-89 has an inverse T command.)
A probability table for the Student’s t-distribution can also be used. The table gives t-scores that correspond to the confidence level (column) and degrees of freedom (row). (The TI-86 does not have an invT program or command, so if you are using that calculator, you need to use a probability table for the Student’s t-Distribution.) When using a t-table, note that some tables are formatted to show the confidence level in the column headings, while the column headings in some tables may show only corresponding area in one or both tails.
A Student’s t table gives t-scores given the degrees of freedom and the right-tailed probability. The table is very limited. Calculators and computers can easily calculate any Student’s t-probabilities.
The notation for the Student’s t-distribution (using T as the random variable) is:
T ~ tdf where df = n – 1.
For example, if we have a sample of size n = 20 items, then we calculate the degrees of freedom as df = n – 1 = 20 – 1 = 19 and we write the distribution as T ~ t19.
If the population standard deviation is not known, the error bound for a population mean is:
EBM = [latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}})(\frac{{\sigma}}{{\sqrt{n}}})[/latex]
- [latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}}[/latex]is the t-score with area to the right equal to[latex]\displaystyle\frac{{\alpha}}{{2}}[/latex],
- degree of freedom, df = n – 1, and
- s = sample standard deviation.
The format for the confidence interval is: ([latex]\displaystyle\overline{x}[/latex] – EBM, [latex]\displaystyle\overline{x}[/latex] + EBM)
In other words, the formula for the confidence interval is
([latex]\displaystyle\overline{x}[/latex] – [latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}})(\frac{{\sigma}}{{\sqrt{n}}})[/latex], [latex]\displaystyle\overline{x}[/latex] + [latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}})(\frac{{\sigma}}{{\sqrt{n}}})[/latex])
Calculate the Confidence Interval bu using TI-Calculator:Press STAT. Arrow over to TESTS.Arrow down to 8:TInterval and press ENTER (or just press 8). |
Example 1
Suppose you do a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects with the results given. Use the sample data to construct a 95% confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data.
The solution is shown step-by-step and by using the TI-83, 83+, or 84+ calculators.
8.6 9.4 7.9 6.8 8.3 7.3 9.2 9.6 8.7 11.4 10.3 5.4 8.1 5.5 6.9
|
Solution A:
To find the 95% confidence interval, you need the sample mean, , and the EBM.
[latex]\displaystyle\overline{X}[/latex] = 8.2267, s = 1.6722, n = 15, df = 15 – 1 = 14
CL = 0.95.
Then α = 1 – CL = 1 – 0.95 = 0.05
[latex]\displaystyle\frac{{\alpha}}{{2}}[/latex] = 0.025
[latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}} = {t}_{0.025}[/latex]
The area to the right of [latex]\displaystyle{t}_{0.025}[/latex] is 0.025, and the area to the left of[latex]\displaystyle{t}_{o.o25}[/latex] is 1 – 0.025 = 0.975
TI-84+ Calculator : invT(.975,14) or use t-table to find [latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}[/latex] when df = 14.
[latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}={t}_{0.025}={2.14}[/latex]
EBM = [latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}})(\frac{{s}}{{\sqrt{n}}})[/latex]
Hence, EBM = [latex]\displaystyle(2.14)(\frac{{1.6722}}{{\sqrt{15}}})=(0.924)[/latex]
[latex]\displaystyle\overline{x}[/latex] – EBM = 8.2267 – 0.9240 = 7.3
[latex]\displaystyle\overline{x}[/latex] + EBM =8.2267 + 0.9240 = 9.15
The 95% confidence interval is (7.30, 9.15).
We estimate with 95% confidence that the true population mean sensory rate is between 7.30 and 9.15.
Solution B
Press STAT
and arrow over toT ESTS
.
Arrow down to 8:TInterval
and press ENTER
(or you can just press8
).
Arrow to Data
and press ENTER
.
Arrow down to List
and enter the list name where you put the data.
There should be a 1 after Freq
.
Arrow down to C-level
and enter 0.95
Arrow down to Calculate
and press ENTER
.
The 95% confidence interval is (7.3006, 9.1527)
| Note: When calculating the error bound, a probability table for the Student’s t-distribution can also be used to find the value of t. The table gives t-scores that correspond to the confidence level (column) and degrees of freedom (row); the t-score is found where the row and column intersect in the table. |
Try It
You do a study of hypnotherapy to determine how effective it is in increasing the number of hourse of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results.
Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data.
8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5
[practice-area rows=”1″][/practice-area]
Show Answer
(8.1634, 9.8032)
Example 2
The Human Toxome Project (HTP) is working to understand the scope of industrial pollution in the human body. Industrial chemicals may enter the body through pollution or as ingredients in consumer products. In October 2008, the scientists at HTP tested cord blood samples for 20 newborn infants in the United States. The cord blood of the “In utero/newborn” group was tested for 430 industrial compounds, pollutants, and other chemicals, including chemicals linked to brain and nervous system toxicity, immune system toxicity, and reproductive toxicity, and fertility problems. There are health concerns about the effects of some chemicals on the brain and nervous system. This table shows how many of the targeted chemicals were found in each infant’s cord blood.
| 79 | 145 | 147 | 160 | 116 | 100 | 159 | 151 | 156 | 126 |
| 137 | 83 | 156 | 94 | 121 | 144 | 123 | 114 | 139 | 99 |
Use this sample data to construct a 90% confidence interval for the mean number of targeted industrial chemicals to be found in an in infant’s blood.
Solution A:
From the sample, you can calculate [latex]\displaystyle\overline{x}[/latex]=127.45
and s = 25.965. There are 20 infants in the sample, so n = 20, and df = 20 – 1 = 19.
You are asked to calculate a 90% confidence interval: CL = 0.90, so [latex]\displaystyle\alpha[/latex]= 1-CL = 1-0.90 = 0.10
[latex]\displaystyle\frac{{\alpha}}{{2}}[/latex]= 0.05
[latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}}={t}_{0.05}[/latex]
By definition, the area to the right of t0.05 is 0.05 and so the area to the left of t0.05 is 1 – 0.05 = 0.95.
Use a table, calculator, or computer to find that t0.05 = 1.729.
EBM = [latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}(\frac{{s}}{{\sqrt{n}}})[/latex]={1.729}([latex]\displaystyle\frac{{25.965}}{{\sqrt{20}}}={10.038}[/latex]
[latex]\displaystyle\overline{x}[/latex] – EBM = 127.45 – 10.038 = 117.412
[latex]\displaystyle\overline{x}[/latex]+EBM= 127.45 + 10.038= 137.488
We estimate with 90% confidence that the mean number of all targeted industrial chemicals found in cord blood in the United States is between 117.412 and 137.488.
Solution B:
Enter the data as a list.
Press STAT
and arrow over toTESTS
.
Arrow down to 8:TInterval
and press ENTER
(or you can just press8
).
Arrow to Data and pressENTER
.
Arrow down to List
and enter the list name where you put the data.
Arrow down to Freq
and enter 1.
Arrow down to C-level
and enter 0.90
Arrow down to Calculate
and press ENTER
.
The 90% confidence interval is (117.41, 137.49).
Example 3
A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in This table. Use this sample data to construct a 98% confidence interval for the mean number of hours statistics students will spend watching television in one week.
| 0 | 3 | 1 | 20 | 9 |
| 5 | 10 | 1 | 10 | 4 |
| 14 | 2 | 4 | 4 | 5 |
Solution A:
[latex]\displaystyle\overline{x}[/latex]= 6.133, s = 5.514, n= 15, and df = 15-1=14
CL = 0.98, so [latex]\displaystyle\alpha[/latex] = 1- CL = 1.0.98 = 0.02
[latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}}={t}_{0.01}[/latex]
[latex]\displaystyle({t}_{\frac{{\alpha}}{{2}}}={t}_{0.01}={2.624}[/latex]
EBM = [latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}(\frac{{s}}{{\sqrt{n}}})[/latex]={2.624}(\frac{{5.514}}{{\sqrt{15}}}={3.736}[/latex]
[latex]\displaystyle\overline{x}[/latex] – EBM = 6.133 – 3.736 = 2.397
[latex]\displaystyle\overline{x}[/latex]+EBM= 16.133 -+3.736= 9.869
We estimate with 98% confidence that the mean number of all hours that statistics students spend watching television in one week is between 2.397 and 9.869.
Solution B:
Enter the data as a list.
PressSTAT
and arrow over to TESTS
.
Arrow down to8:TInterval
.
PressENTER
.
Arrow toData
and pressENTER
.
Arrow down and enter the name of the list where the data is stored.
EnterFreq
: 1Enter C-Level
: 0.98
Arrow down toCalculate
and pressEnter
.
The 98% confidence interval is (2.3965, 9,8702).
References
“America’s Best Small Companies.” Forbes, 2013. Available online at http://www.forbes.com/best-small-companies/list/ (accessed July 2, 2013).
Data from Microsoft Bookshelf.
Data from http://www.businessweek.com/.
Data from http://www.forbes.com/.
“Disclosure Data Catalog: Leadership PAC and Sponsors Report, 2012.” Federal Election Commission. Available online at http://www.fec.gov/data/index.jsp (accessed July 2,2013).
“Human Toxome Project: Mapping the Pollution in People.” Environmental Working Group. Available online at http://www.ewg.org/sites/humantoxome/participants/participant-group.php?group=in+utero%2Fnewborn (accessed July 2, 2013).
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Concept Review
In many cases, the researcher does not know the population standard deviation, σ, of the measure being studied. In these cases, it is common to use the sample standard deviation, s, as an estimate of σ. The normal distribution creates accurate confidence intervals when σ is known, but it is not as accurate when s is used as an estimate. In this case, the Student’s t-distribution is much better. Define a t-score using the following formula:
[latex]\displaystyle\frac{{\overline{x}-\mu}}{{\frac{{s}}{{\sqrt{n}}}}}[/latex]
The t-score follows the Student’s t-distribution with n – 1 degrees of freedom. The confidence interval under this distribution is calculated with EBM = [latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}(\frac{{s}}{{\sqrt{n}}})[/latex] where[latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}[/latex]s the t-score with area to the right equal to [latex]\displaystyle\frac{{\alpha}}{{2}}[/latex] s is the sample standard deviation, and n is the sample size. Use a table, calculator, or computer to find [latex]\displaystyle\frac{{\alpha}}{{2}}[/latex] for a given a.
Formula Review
s = the standard deviation of sample values.
t = [latex]\displaystyle\frac{{\overline{x}-\mu}}{{\frac{{s}}{{\sqrt{n}}}}}[/latex]
s the formula for the t-score which measures how far away a measure is from the population mean in the Student’s t-distribution
df = n – 1; the degrees of freedom for a Student’s t-distribution where n represents the size of the sample
T~tdf the random variable, T, has a Student’s t-distribution with df degrees of freedom
s the formula for the t-score which measures how far away a measure is from the population mean in the Student’s t-distribution
df = n – 1; the degrees of freedom for a Student’s t-distribution where n represents the size of the sample
T~tdf the random variable, T, has a Student’s t-distribution with df degrees of freedom
[latex]\displaystyle{t}_{\frac{{\alpha}}{{2}}}(\frac{{s}}{{\sqrt{n}}})[/latex] = the error bound for the population mean when the population standard deviation is unknown
is the t-score in the Student’s t-distribution with area to the right equal to
The general form for a confidence interval for a single mean, population standard deviation unknown, Student’s t is given by (lower bound, upper bound)
= (point estimate – EBM, point estimate + EBM) = [latex]\displaystyle(\overline{x} -\frac{{ts}}{{\sqrt{n}}},\overline{x} +\frac{{ts}}{{\sqrt{n}}})[/latex]


8.2 Interdisciplinarity and Learning Communities
A learning community, according to Goodyear, De Laat, and Lally, is a group of people who meet regularly and share common academic goals and attitudes[6]. Learning communities tend to place importance on academic competency. In addition, they possess shared emotional connections and active involvement in learning professionally and personally. In many ways, it is a more focused approach towards the development of interpersonal relationships, and goes beyond academics by blending theories from many different areas outside of the structured disciplines.
This is common in institutes of higher learning, given the psycho-social development that occurs for students during their post-secondary educational student experiences. Students in higher education tend to engage in different courses that broaden their horizons. For example, a group of students in an education program develop a cohesive working and personal relationship, and decide to take a political-science course about Canadian elections. As a cohesive, personal group, these students are engaging in, and learning, new content together. They also bring theories back to their own educational discipline to further explore interdisciplinary connections.
This macro view can lead to their final capstone project or thesis. In many ways, the college/university experience of academics, clubs, friendships, and those who gather for knowledge is a form of interdisciplinarity. These connections go beyond the classroom. Moving forward, the concept of interdisciplinarity can be an important phenomenon to improve the understanding of the communities within a college or university, both inside and outside the classroom.


27 Student Clinical Evaluation Policy
- CPs will send out all student evaluations
- Once a tech completes an evaluation, the student will be able to see it as “completed” but will not be able to open it
- CPs must review all evaluations and then release them to the students in order for students to open them
- Students must agree or disagree with all evaluations that asks this question
- Grades will be delayed at the end of the semester if a student has not provided agree/disagree on an evaluation
- Approximately five evaluations are sent out on each student each semester unless the student is in his/her second year doing modality rotations.
Failed Clinical Evaluations
Students are expected to earn a passing grade in all clinic rotations within a clinical experience course. Clinical rotation passing scores are specified in the syllabus and on the grade form for each clinical course. Students must receive at least a C course grade in order to pass a clinical experience course. Note: a C- is considered a failing grade.
Failing scores for two (2) clinical rotations in a clinical experience course will result in automatic course failure, even if the cumulative scores for all rotations results in a passing score. A clinical experience course failure results in Program Probation for failure to progress.
Clinical competencies earned during failed clinical rotations will be removed from the clinical database and not counted for course productivity or toward graduation requirements.