Question

10.7 When people make estimates, they are influenced by anchors to their estimates. 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 in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. (Data extracted from “Drilling Down, Sizing Up a Cheeseburger’s Caloric Heft,” The New York Times, October 4, 2010, p. B2.) Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 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.b. In the context of this study, what is the meaning of the Type I error? c. In the context of this study, what is the meaning of the 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?

Answer 1

Answer:

Answer: A)H0:mul-mu2-0 (there is no difference in mean estimated amount of calories irn cheeseburger for people who thought about cheesecake first than for the people who thought about organic fruit salad first) Hlmul-mu2<0 (the mean estimated amount of calories in cheeseburger for people who thought about cheesecake first is lower than for the people who thought about organic fruit salad first) Where, mul and mu2 denotes population mean estimated calories in cheeseburger for people who thought about cheesecake first and who thought about organic fruit salad first. B) TypeI error refer to incorrect rejection of true null hypothesis. Therefore, if someone, wrongfully reject H0, and conclude that the mean estimated amount of calories in cheeseburger for people who thought about cheesecake first is lower than for the people who thought about organic fruit salad first, then she is supposedly committed Type I error C) Type II error means failure to reject a false null hypothesis. If someone, wrongfully conclude there is no difference in mean estimated amount of calories in cheeseburger for people who thought about cheesecake first than for the people who thought about organic fruit salad first, when actually the mean estimated amount of calories in cheeseburger for people who thought about cheesecake first is lower than for the people who thought about organic fruit salad first, then she is supposedly committed a Type II error

D)

The test statistic for testing the null hypothesis is given by x,-x, STAT

from normal populations variances, we can use the pooled-variance t-test. To begin the test we first calculate the pooled variance. 19x1282 +19x1402 Pooled variance 19+19 311296 +372400 38 17992

Put the values in t-statistic what we have need for this calculation. Now we get the test statistic: (780-1041)-0 STAT 17992x |-+ 20 20 261 17992 x(0.1) -261 1799.2 6.1532 =1-61532

Critical value: The tsrar statistic follows a distribution with n, +n2-2 degree of freedom. Here 20+20-2 - 38 And test is left tailed so the critical value is given by-,(aM+n2-2), where α is level of where a is level of significance Now by using the distribution tables we have -(o13).4286 (0.01,38)

Critical region: if the t-test statistic < (ad) , d.f Critical region fort this test is defined as: ISTAT <-(0.01.38 Hence, the value of statistic-6.1532 is falling in the critical region; therefore, there is enough evidence available to reject the null hypothesis and to accept that the mean estimated amount than for the people who thought about the organic fruit salad first