The p-value for the two-sided hypothesis test is 0.04. How would you interpret the p-value?

Question

The owner of an ice cream shop wants to determine whether there is a relationship between ice cream sales and temperature. The owner collects data on temperature and sales for a random sample of 30 days and runs a regression to determine if there is a relationship between temperature (in degrees) and ice cream sales. The p-value for the two-sided hypothesis test is 0.04. How would you interpret the p-value?

1)If there is no relationship between temperature and sales, the chance of selecting a sample this extreme would be 4%.

2)If there is a relationship between temperature and sales, the chance of seeing a regression coefficient this large would be 4%.

3)There is a 4% chance that there is a relationship between temperature and revenue.

4)There is a 4% chance that there is no relationship between temperature and revenue.

Answer 1

Choice 1 most closely represents the interpretation of a p-value:

”1)If there is no relationship between temperature and sales, the chance of selecting a sample this extreme would be 4%.”

The p-value is the probability of obtaining a test statistic (or sample statistic) at least as extreme as the observed statistic, assuming the null hypothesis is true.

In this question the null hypothesis is that there is no relationship (presumably linear since the question doesn’t have enough detail) between sales and temperature. The alternative hypothesis is that there is a relationship between sales and temperature.

To number 1, I would only make one modification:

”1)If there is no relationship between temperature and sales, the chance of selecting a sample this extreme or more extreme would be 4%.”

This improves the accuracy of option 1. Even without this addition, choice 1 is still the most correct answer. The other answer choices are common misinterpretations of p-values.

For reference see: https://link.springer.com/article/10.1007/s10654-016-0149-3