The professor would say that if the p-value is less than or equal to the level of significance (denoted by alpha) we reject the null hypothesis because the test statistic falls in the rejection region.When I first learned this, I did not understand why were comparing the p values to the alpha values..
Thus we reject the null hypothesis if p value is less than alpha and we fail to reject if p value is equal or more than alpha.You reported it vice versa. Of course in practice this will make. very little difference. I mean if I get a p value of exactly 0.05 then I will probably repeat the experiment. This still doesn't explain why a statistician can't say we accept the null hypothesis, as a certain unnamed, wet-behind-the-ears, statistically-challenged editor might have suggested to Tiny. Once. Here's the bottom line: even if we fail to reject the null hypothesis, it does not mean the null hypothesis is true. If the p value is 0.02 then one could reject the null hypothesis with a 98% degree confidence level against a type I error. On the other hand if the p value is 0.07 than the confidence level against a type I error is only be 93%, somewhat below the 95% confidence level. Definition: Assuming that the null hypothesis is true, the p value is the probability of obtaining a sample mean as extreme or more extreme than the sample mean actually obtained. A small p value associated with a sample mean indicates a rare occurrence and would lead one reject the null hypothesis. In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis.  In statistics, why do you reject the null hypothesis when the p-value is less than the alpha value (the level of significance). up vote 2 down vote favorite. 1. This is a question that I've always wondered in statistics, but never had the guts to ask the professor. The professor would say that if the p-value is less than or equal to the level of significance (denoted by alpha) we reject the null hypothesis because the test statistic falls in the rejection region. When I first learned this, I did not understand why were comparing the p values to the alpha values 1 A Type II error occurs when the researcher fails to reject a null hypothesis that is false. 2  The probability of committing a Type II error is called Beta, and is often denoted by β. 3  The probability of not committing a Type II error is called the Power of the test. Two types of errors can result from a hypothesis test. 1  Type I error. 2  A Type I error occurs when the researcher rejects a null hypothesis when it is true. 3  The probability of committing a Type I error is called the significance level. 4  This probability is also called alpha, and is often denoted by α. 5  Type II error. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. 6.If the test statistic lies in the critical region, reject the null hypothesis in favor of the alternative hypothesis, if it does not, then you would fail to reject the hull hypothesis. To save time and effort the table below relates critical z values to alpha levels and type test. Definition: Assuming that the null hypothesis is true, the p value is the probability of obtaining a sample mean as extreme or more extreme than the sample mean actually obtained. A small p value associated with a sample mean indicates a rare occurrence and would lead one reject the n If we assert that the independent variable has an effect (we reject the null hypothesis and accept the research hypothesis) when in fact it does not, we commit an error. This is called a Type 1 error, and the probability of committing it is equal to the alpha level. However, we can make another kind of error.  If the P-value is less than the significance level, we reject the null hypothesis. Region of acceptance. The region of acceptance is a range of values. If the test statistic falls within the region of acceptance, the null hypothesis is not rejected. Two types of errors can result from a hypothesis test. 1  Type I error. 2  A Type I error occurs when the researcher rejects a null hypothesis when it is true. 3  The probability of committing a Type I error is called the significance level. 4  This probability is also called alpha, and is often denoted by α. 5  Type II error. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it. In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population.
http://blog.minitab.com/blog/understanding-statistics/things-statisticians-say-failure-to-reject-the-null-hypothesis http://fsweb.bainbridge.edu/dbyrd/statistics/hypothesistesting.htm http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/hypothesis-tests/basics/what-is-a-critical-value/ http://math.stackexchange.com/questions/582945/in-statistics-why-do-you-reject-the-null-hypothesis-when-the-p-value-is-less-th http://stattrek.com/hypothesis-test/hypothesis-testing.aspx https://statistics.laerd.com/statistical-guides/hypothesis-testing-3.php http://fsweb.bainbridge.edu/dbyrd/statistics/hypothesistesting.htm http://pirate.shu.edu/~hovancjo/exp/null_hypo.htm http://stattrek.com/hypothesis-test/hypothesis-testing.aspx https://statistics.laerd.com/statistical-guides/hypothesis-testing-3.php
why would you reject the null hypothesis