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ECO 252 Fall 2000 Formulas Second Exam Dr. Andrews x n x s n p (1 ) n Introductory information: (this is not a question) A company is trying to decide whether to change advertising companies. They compare a trial company’s results to their current company, and decide whether or not to switch. The following problems are each separate ways to test the same idea. Part I. 5 points each: 1. 2. 3. 4. Set up the null and alternative hypothesis in words. What is the type I error in this case? What is the type II error in this case? What is an appropriate level of α? Explain your answer. Part II. 10 points each Irrespective of your answer in 4, use α= .05 for the remainder of the exam. For each problem state the null and alternative hypotheses in symbols, show all your work, and interpret your results. A p-value calculation is only required for the second test. (The conclusion you reach may differ for different approaches, i.e., you may reject in one test and fail to reject in another.) Test One: Over the past several years our current advertisement is seen by an average customer .3 times each week with a standard deviation of 2 times. In a test of the new advertiser, 36 individuals saw the advertisement an average of .4 times per week with a standard deviation of 5 times. Explain why it is absolutely necessary to sample at least 30 customers for this test. Test Two: In a sample of 64 individuals 24 had seen our current ad at least once in the last week while 35 had seen the new advertiser’s ad at least once in the last week. For this question, also calculate and interpret the p-value. Test three: To test recall, 5 individuals were asked 8 questions about the advertisements the day after they had been exposed to the ad. The number of correct responses is recorded below. Extra columns are added for your convenience, use whichever ones you want. Person Old ad New ad 1 8 7 2 7 7 3 6 8 4 2 4 5 5 8 Hypothesis testing two samples Two Samples Means Proportions H o : 1 2 0 p1 p2 p1 (1 p1 ) p2 (1 p2 ) n1 n2 TS CV Z Independent H o : 1 2 ? 0 Dependent H o : d ? 0 d sd n CV t ,n 1 TS Ho :1 2 TS 2 s LG 2 s sm CV F.10,( nto p 1),( nb o t 1) REJ Unequal TS x1 x 2 s12 s 22 n1 n2 CV Z FTR equal TS s 2p x1 x 2 1 1 s 2p ( ) n1 n2 (n 1 1) s12 ( n2 1) s 22 n1 n2 2 CV t ,n n 2