Question

A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a​ calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated was 783 for the group that thought about the cheesecake and 1005 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 students in each​ group, and the standard deviation of the number of calories estimated was 125 for the people who thought about the cheesecake first and 145 for the people who thought about the organic fruit salad first.

a. State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first. Let μ1 represent the mean number of calories estimated by the people who thought about the cheesecake first and μ2 represent the mean number of calories estimated by the people who thought about the organic fruit salad first.

b. In the context of this​ study, what is the meaning of a Type I​ error?

c. In the context of this​ study, what is the meaning of a Type II​ error?

d. At the 0.01 level of​ significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad​ first?

e. Find the test statistic.

f. Find the​ p-value.

g. State the conclusion of the test.

h. If you were developing a commercial for a​ cheeseburger, based on the results of​ (d), what other foods might you show in the​ commercial?

Answer 1