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 avgbig 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.

1. Option 1: d = 5. Option 2: d = 10 An observed difference of d = 10 is more extreme than d = 5. Hence, the p-value of d = 10 should be smaller.
2. 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, a larger sample size results in a larger statistic. A larger statistic , in turn, will have a smaller p-value. So, a sample size of 300 will have a smaller p-value.
3. Option 1: d = —10. Option 2: d = 10 Assuming that the sample size is the same in both samples, there is no difference because both values of d are the same (in absolute terms). They will have the same p-value; the difference will be just in the tails of the distribution (either the left tail or the right tail).

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