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 781 for the group that thought about the cheesecake and 1026 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 129 for the people who thought about the cheesecake first and 150 for the people who thought about the organic fruit salad first. Complete parts (a) through (e) below. 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 , represent the mean number of calories estimated by the people who thought about the cheesecake first and J2 represent the mean number of calories estimated by the people who thought about the organic fruit salad first. Choose the correct answer below. O A. Ho: H1 2 H2 OB. HO: H1 # H2 H1: H1 =H2 H1: 41 = H2 O C. Ho: H1 = H2 OD. HO: Hq SH2 Hy: Hy # H2 H1 : Hq > H2 b. In the context of this study, what is the meaning of a Type I error? O A. 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. O B. 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. O 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. O D. A Type I error is committed if the alternative hypothesis is rejected but the mean estimate is not significantly lower for the people who thought about the cheesecake.c. In the context of this study, what is the meaning of a Type II error? O A. 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. O 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. O C. 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. O D. A Type II error is committed if the alternative hypothesis is rejected but the mean estimate is significantly lower for the people who thought about the cheesecake. d. At the 0.05 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. tSTAT = (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) State the conclusion of the test. Ho. There 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 firste. If you were developing a commercial for a cheeseburger, based on the results of (d), what other foods might you show in the commercial? O A. Show the cheesecake before showing the cheeseburger, so that the cheeseburger will appear healthier. O B. Show both the cheesecake and the organic fruit salad after showing the cheeseburger, so that the cheeseburger will appear healthier. O C. Show both the cheesecake and the organic fruit salad before showing the cheeseburger, so that the cheeseburger will appear healthier. O D. Show the organic fruit salad before showing the cheeseburger, so that the cheeseburger will appear healthier