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Part 1
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 776 for the group that thought about the cheesecake and 914 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 147 for the people who thought about the organic fruit salad first. Complete parts (a) through (e).
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Part 1
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 mu 1 represent the mean number of calories estimated by the people who thought about the cheesecake first and mu 2 represent the mean number of calories estimated by the people who thought about the organic fruit salad first. Choose the correct answer below.
A.
Upper H 0: mu 1 equals mu 2
Upper H 1: mu 1 not equals mu 2
B.
Upper H 0: mu 1greater than or equalsmu 2
Upper H 1: mu 1less thanmu 2
C.
Upper H 0: mu 1less than or equalsmu 2
Upper H 1: mu 1greater thanmu 2
D.
Upper H 0: mu 1 not equals mu 2
Upper H 1: mu 1 equals mu 2
b. In the context of this study, what is the meaning of a Type I error?
A.
A Type I error is committed if one rejects both the null and alternative hypotheses.
B.
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.
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.
D.
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. In the context of this study, what is the meaning of a Type II error?
A.
A Type II error is committed if one does not reject both the null and the alternative hypothesis.
B.
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.
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.
D.
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.
d. Assume the population variances are not equal. At the 0.10 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.
t Subscript STATequals
enter your response here (Round to two decimal places as needed.)
Find the p-value.
p-valueequals
enter your response here (Round to three decimal places as needed.)
State the conclusion of the test.
▼
Reject
Do not reject
H Subscript 0. There
▼
is insufficient evidence
is 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 first.
e. A psychologist now informs us that these 2 groups are independent, and that the population standard deviation for both groups is 140. What is the value of the Z-statistic for the test of the hypothesis that the 2 groups have equal mean numbers of estimated calories?
Upper Z Subscript stat Baseline equals
enter your response here (Round to three decimal places as needed.)
