Question

A fast food chain has been accused of trying to save money by reducing the number of fries in your order when you purchase them in big size. As a stat 2 student, you’re prepared to test these allegations. The parameter you are interested in is:

d = avg_regular − avg_big

where avg_regular is the average number of fries in a regular order, and avg_big is the average number of fries in a big-size order. Your null hypothesis is that d = 0 and your alternative hypothesis is that d > 0. In each of the following scenarios, indicate in which of the options you expect to have a smaller p-value, or whether there is no difference. Explain your reasoning.

a. Option 1: d = 5. Option 2: d = 10

b. Option 1: you take 30 samples of each type of fry. Option 2: you take 300 samples of each type of fry. Assuming that the value of d is the same in both samples.

c. Option 1: d = −10. Option 2: d = 10. Assume that the sample size is the same in both samples.

Answer 1