252grass3-071 3/08/07 (Open this document in 'Page Layout' view!)Name: Class days and time:Please include this on what you hand in!Graded Assignment 3Part 1. In your outline there are 6 methods to compare means or medians, methods D1, D2, D3, D4, D5a and D5b. Methods D6a and D6b compare proportions and method D7 compares variances or standard deviations. In the following cases, identify 0H and 1H and identify which method to use. Method E1 is a chi-squared test that compares multiple proportions. Method F1 is analysis of variance (ANOVA), which compares multiple means. If the hypotheses involve two means, state the hypotheses in terms of both and 21D. If the hypotheses involve two proportions, state them in terms of both p and 21ppp . If the hypotheses involve two standard deviations or variances, state them in terms of both 2 and 2221 or 2122. All the questions involve means, medians, proportions or variances. One of these problems is a chi-squared test.Note that Problem D8 is a similar assignment to that below.Note: Look at 252thngs (252thngs) on the syllabus supplement part of the website before you start (and before you take exams). Neatness and clarity of explanation are expected. Note that from now on neatness means paper neatly trimmed on the left side if it has been torn, multiple pages stapled and paper written on only one side.-----------------------------------------------------------------------------------------------------------------------------Example: This may seem long but it appears on a previous graded assignment 3. A group of supervisors are given exams on management skills before and after taking a course in management. Scores are as follows.Supervisor Before After 1 63 78 2 93 92 3 84 91 4 72 80 5 65 69 6 72 85 7 91 99 8 84 82 9 71 81 10 80 87 11 68 93 If we assume that the distribution of results is Normal, what method should we use to answer the question“Has the course improved the scores of the managers?” What are our hypotheses?Solution: You are comparing means before and after the course. You can get away with using means because the parent distributions are Normal. If 2 is the mean of the second sample, you are hoping that12, which, because it contains no equality is an alternate hypothesis. So your hypotheses are211210::HH or 0:0:211210HH. If 21D, then 0:0:10DHDH. The important thing to noticehere is that the data are in before and after pairs, so you use Method D4.In most of these problems you have to define what you mean by group or sample one and group 2. For example in problem 3 you will probably let 1x be earnings of corporate lawyers and 2x be the earningsof private practice lawyers. 1. You have profit rates, 1x, for a sample of the European operations of 20 pharmaceutical firms. You also have profit rates, 2x, for the American operations of the same 20 firms. You believe that they are normally distributed and you wish to see whether the European firms were more profitable than the American firms.2. You have a sample of 15 US cities, with a typical salary for a corporate lawyer and a typical salary for a lawyer in private practice. You wish to compare the earnings of the two types of lawyers. You do not believe that the underlying distribution is Normal.3. You have a sample of the earnings of 43 randomly chosen corporate lawyers and another independent sample of salaries of 43 lawyers in private practice. You wish to show that the average corporate lawyer makes more than the average lawyer in private practice. You believe that the parent (underlying) distribution is normal and you think that you know the population variances for each group.4. You find out that you were wrong about the variances in problem 3 and have to recompute the variancesof the salaries for each of the two groups in Problem 3 from the samples that you had gathered. First you wish to compare the reliability of earnings for the two groups.5. Your null hypothesis in Problem 4 was rejected and you, once again, are trying to show that corporate lawyers make more than lawyers in private practice.6. Royal Crown Cola recruits a panel of 115 men and 56 women. The entire group is polled to see if they like the current formulation of Royal Crown better than Coca Cola. Then they are asked to compare a newformulation of Royal Crown against Coca Cola. Our data consists of the number of each panel member and whether 1) each member liked Royal Crow better than Coke originally and 2) whether each member liked Royal Crown Better than Coke with the new formulation for Royal Crown. Has the new formulation improved the sales prospects of Royal Crown?7. Using the panel above and only the new formulation, the numbers of men and women who preferred Royal Crown is tabulated separately and the data is examined to see if gender plays a role in preferences. 8. In addition to the 115 men and the 56 women, the Royal Crown people find 45 monsters to tell them whether they prefer the new formulation of RC to Coke. We wish to compare the preferences of the three groups.9. A group of 25 male accountants with working wives was asked to rate their job satisfaction on a 1 to 10 scale. Another group of 20 male accountants whose wives do not work were also asked to rate their satisfaction. We want to test whether the satisfaction of accountants with working wives is below that of those whose wives do not work and do not want to use a method that assumes an underlying Normal distribution.Part 2. Do problems 6 and 7 using the following data. Men WomenLiked 1st, liked 2nd 12 8Liked 1st, didn’t like 2nd 3 3Didn’t like 1st , liked 2nd 5 3 Didn’t like 1st , didn’t like 2nd 95 42Total 115 56Part 3. (Extra Credit) Invent and solve 4 problems. One each for methods D1 thru
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