MGEB12 – Quantitative Methods in Economics-II

Part A (Long Questions) Question-1 (10 Points) The food label on a cookie bag states that there is at most 2 grams of saturated fat in a single cookie. In a sample of 36 cookies, it is found that the mean amount of saturated fat per cookie is 2.1 grams and that the standard deviation is 0.25. a) [6 Points] State the null and alternative hypotheses. Using the p-value approach, test the hypothesis at the 1% level of significance. Solution: 2.4 36 0.25 2.1 2 : 2 : 2 35 1 0      t H H   P-Value: Since t statistics falls between t0.01,35= 2.438 and t0.025,35 = 2.030, the p-value will be between 1% and 2.5%. Decision: Since the p-value is more than than 1%. We cannot reject the null. Therefore, we cannot conclude the alternative. Page 3 of 23 b) [4 Points] Explain in no more than there sentences what Power of the test is. Without calculation, what do you think the power of the test in part (a) would be if the alternative