Answers to Practice Questions for Final:

(annotated with side comments in places)


Part I: Review of Basics: Hypothesis testing

1. Piano lesson problem

a. Do piano lessons improve spatial skills in children?

b. Piano lessons (this is what experimenter controls, expected to be the "cause")

c. Spatial skills (this is something experimenter measures, DV is what should show the "effect")

d. 3 months lessons / no lessons ..... or just lessons / no lessons

e. Ha: Mu-lessons not equal to Mu-no lessons

Ho: Mu-lessons = Mu-lessons

Note: the research question focuses on "improvement" so looks directional. Now, in this case, a change in the opposite direction is both plausible and would be interesting. So a 2-tailed test would be the best choice. However, if you decide to test this using directional hypotheses, be sure and be consistent--directional hypotheses, one-tailed test, single critical region/value etc. Don't switch back and forth as you proceed through the problem. For directional, be sure the two hypotheses cover all possibilitis:

Ha: Mu-lessons > Mu-no lessons & Ho: Mu-lessons < or = Mu-lessons

I wouldn't count that as incorrect.

f. t-test for independent means [for independent samples also okay -- same test, different name]

Note: Why independent? You have two DIFFERENT sets of children, some who get lessons, some who don't. A dependent means approach would be to give all the children lessons, and test them both before and after. Same research question, different approach to collecting data.

g. .05 or .01 (both are standard choices).

What it measures: the significance level, chance of Type I error (a false positive).

For .05, chance is 5%, for .01, chance is 1%

Note: Because this is a small n experiment, .05 will give a better balance between chance of Type I and Type II errors. .01 will give you a very low power test.

h. Conclude that piano lessons have an effect on spatial skills, with confidence level of 95% (or 99% if you chose alpha = .01).

Note: To know whether spatial skills were improved or worsened by piano lessons, would need to look at the sample means. Don't automatically conclude that significant result shows improvement!

i. No. Results are inconclusive. There is always some chance of a Type II error. Power is low because of small n (only 20 in each group).

j. Use larger samples.

Other correct answers: If you had .01 alpha, change to .05 alpha.

Give piano lessons for a longer time to strengthen the effect (increase effect size)

Symbols and formulas:



sample mean


significance level / probability of Type I error

degrees of freedom

chi-square [note: there should not be a line under the sum sign--this is a type!: you do the (O-E)2/E calculation for each cell, and then sum the results]

bivariate regression [prediction also okay, would be counted correct if you just said regression, too]

population variance / estimated population variance

degrees of freedom for chi-square independence (if you just said chi-square, would get half points)

S2/ sigma2

proportion of variance accounted for [Note: book uses little r2 when doing bivariate regression, capitalized R2 for multiple regression, multiple correlation. Don't need to worry about this--just proportion of variance accounted for is fine. But for those who might have noticed, that's what the difference is. Literature is not especially consistent in its use of big and little r, so doesn't deserve too much attention.]