Statistics: Meaning of Alpha

Objectives

• Students will recognize that the alpha value (significance level of a test) is the relative frequency for sample statistic values that lead to a “reject the null” conclusion, given that the null hypothesis is actually true.
• Students will recognize that a given sample mean can lead to a “reject the null” or “fail to reject the null” depending on the alpha level.

Vocabulary

• alpha level
• population
• samples
• sampling distributions of sample means
• significance level

About the Lesson

This lesson involves beginning with a null hypothesis specifying the mean of a normally distributed population with a given standard deviation.
As a result, students will:

• Generate a sample and sample mean and predict whether the sample might reasonably have come from the hypothsized population, considering the criteria they would use to make a decision.
• Consider a fixed alpha level (0.1) and predict the likelihood of getting by chance an outcome at least as extreme as the value determining the border of the rejection region if the null hypothesis is true.
• Generate 100 samples, and observe how many fall into the rejection region to observe that the decision to reject or not to reject the null hypothesis will change depending on alpha.