Calculus: What is a p-value?

Objectives

• Students will recognize that a p-value only has meaning if the null hypothesis is true (a conditional probability).
• Students will interpret a p-value in given contexts as the relative frequency for sample statistic values at least as extreme as that from the observed sample, assuming that the null hypothesis is true.
• Students will recognize the relationship between sample size and p-values: in general, for sample means giving p-values less than 0.5, increasing the sample size decreases the p-value.

Vocabulary

• alpha value
• population
• relative frequency
• sample mean
• sample size
• sample standard deviation
• sampling distribution

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 an observed outcome (a sample of fixed size), which determines a p-value. That value is represented by a shaded region in the sampling distribution.
• Generate additional samples of the same size from the hypothesized population and observe where the means of these samples fall.
• Estimate the likelihood of getting by chance an outcome at least as extreme as the original observed sample mean from the graph of the simulated sampling distribution of sample means that were generated if the null hypothesis is true.