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Quantitative Analysis � International and Public Affairs

This document covers quantitative analysis methods applied to international and public affairs.

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    1 Quantitative Analysis – International and Public Affairs U6500 Sections 1, 2, 3, 4/Fall 2015 Professor Yang Homework #8 : Inference for one mean, Difference in two means, one proportion , and Difference in two proportions Due in Mailbox 49 6 th Floor IAB : Wednesday November 11 4:00 p.m. (Sections 3 & 4 )/ Thursday November 17 4:00 p.m. (Sections 1 & 2 ) 52 points total 1. (8 points total ) Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly fro m bag to bag . Assume net weights are Normally distributed. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H 0 :  = 14 versus H a :  < 14. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of 13.88 oz . with a sample standard deviation of 0.24 oz. a. What is the value of the test statistic? 13.88 14 Test statistic, 2 0.24 16 x t s n        b. What is the critical value at the .05 significance level for this test? Infer the p - value from the table. The critical value at the .05 significance level for this test is – 1.753. The p - value is in between 0.025 and 0.05. c. What is your conclusion (again, assume significance level of .05)? Briefly explain your conclusion (citing your observed test statistic and p - value and what you are comparing these against) . Since the observed test statistic, t = – 2 < – 1.753, reject the null hypothesis at .05 level. The reported results provide enough evidence to conclude that the mean net weight is less than advertised, t (15) = – 2.00, p = .032 < .05. 2. (8 points total ) A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained a simple random sample of 60 high school students in a large suburban school district and found the mean time spent in

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