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 771 for the group that thought about the cheesecake and 1008 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 124 for the people who thought about the cheesecake first and 147 for the people who thought about the organic fruit salad first. Complete parts​ (b) through​ (d).

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

A. Type I error is committed if the null hypothesis is rejected but the mean estimate is significantly lower for the people who thought about the cheesecake.

B. A Type I error is committed if one rejects both the null and alternative hypotheses.

C. A Type I error is committed if one concludes that the mean estimate is significantly lower for the people who thought about the cheesecake when it is not significantly lower.

D. A Type I error is committed if one concludes that the mean estimate is not significantly lower for the people who thought about the cheesecake when it is significantly lower.

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

A. A Type II error is committed if one concludes that the mean estimate is significantly lower for the people who thought about the cheesecake when it is not significantly lower.

B. A Type II error is committed if the null hypothesis is rejected but the mean estimate is not significantly lower for the people who thought about the cheesecake.

C. A Type II error is committed if one does not reject both the null and the alternative hypothesis.

D. A Type II error is committed if one concludes that the mean estimate is not significantly lower for the people who thought about the cheesecake when it is significantly lower.

d. Assume the population variances are not equal. 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? Find the test statistic.

e. Find the p-value.

p-value=

(Round to three decimal places as needed.)

f. State the conclusion of the test.

Reject or Do not reject H0. There is Insufficient evidence or Evidence that the mean number of estimated 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 firs

Answer 1

b) Type I Error is rejecting the null when it is true.

Type II Error is failing to reject the null when it is false.

Hypothesis that can be formed is

group 1 is the people who thought about the cheesecake

group 2 the people who thought about the salad

option C is right

A Type I error is committed if one concludes that the mean estimate is significantly lower for the people who thought about the cheesecake when it is not significantly lower.

c) option D is right

A Type II error is committed if one concludes that the mean estimate is not significantly lower for the people who thought about the cheesecake when it is significantly lower.

d)

e)

reject H0. There is sufficient evidence that the mean number of estimated 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 firs