hw.2Pop.prop.4Topics

hw.2Pop.prop.4Topics - 11/30/2010 hw.2Pop.prop.4Topics.doc...

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Unformatted text preview: 11/30/2010 hw.2Pop.prop.4Topics.doc Two-Population Proportions 4 Topics Page 1 TWO-POP Proportions, 4 topics Revised 11/30/10 In order to get the Expected Values, you may USE the provided XLS file (on the website): 2SampProp.Compute.STUDENT.xls and choose which type of problem you are doing (2x2, 2x3, 3x4) by selecting the tab at the bottom of the Excel file. Be sure to fill in the values ONLY in the body of the table (NOT the totals in the margins). You should create appropriate headings. A. CASE 1: NOTE: The Z version of the difference in population proportions may already have been assigned (hw.2Pop.Prop.ZOnly.pdf ). If so, no need to do it again, and thus skip part A and do Parts B, C, and D. If it has NOT been assigned already, then of course do that part, too. Company 1 (population 1) uses one way to make its employees aware of policies, and Company 2 (population 2) uses another way. We wonder if the two methods are different. In a sample of 200 from company 1, 150 were aware of the policy change. In a sample of 100 from company 2, 86 were aware of the policy change. Using Z, assume the standard deviation you will use without modification is 0.049 and use this as the denominator without any adjustment. CI: Estimate the difference between p1 and p2 by using a 95% confidence interval. 1. This is a CI for what? 2. Construct the CI. 3. Give interpretation HYPOTHESIS TESTING Recall the 5-steps are: Hypos; CV(s); DRule; Decision; Conclusion in terms of the problem. 1. What is the symbol for the standard deviation? 2. Use the regular method and 5 steps to test at α=0.05 whether the proportion at company 1 who were aware is smaller than the proportion at company 2. (Of course, you have to state this as a difference: p1 - p2 [≥.or ≤ or > or <) 0 . (Note that in this class p1 will always be first, so we'll never have an hypothesis of the form p2 - p1 .) Provide a fully completed graph. Pay particular attention to the conclusion in terms of the problem. NOTE THAT FOR TWO POPULATIONS WE WILL TYPICALLY HAVE A TWO-TAILED TEST OF THE DIFFERENCE = 0 VERSUS IT DOESN'T = 0. HOWEVER, AS A REMINDER OF PREVIOUS HYPOTHESES, THIS TIME WE'LL DO A ONE-TAILED TEST. THIS IS ONE OF THE HYPOTHESES: p1 - p2 < 0 AND YOU DECIDE 3. 4. B. WHICH HYPOTHESIS IT IS. Compute the p-value and show where it is on the graph. Do the test using STS and label the graph. (Using Z we can do both regular and STS but here we only are doing STS. With χ STS is the only choice – there is no regular method). Same data as part A, but now using χ2: assume df=1 . Test whether the two population proportions are the same (which is different from the previous problem), and it is a 1-tailed test. (You'll need to rewrite the given information as a contingency table, as we had in class, where do not use proportions directly, but rather use the actual raw data. How to do this: for sample 1 the sample size is 200 and 150 were aware, so 50 were not aware. Sample 2 of 100, 86 were aware and 14 were not aware.) a. For the χ2: Have we met the assumption about expected values? EACH expected value must be ≥ 5 for this method to be valid. b. Note that there is no "regular" method; the only hypothesis testing method for this case is STS. c. Compute the p-value and show it on the graph. Continued on next page 11/30/2010 Two-Population Proportions 4 Topics Page 2 C. New Data and new problem: Here population 1 is Honda owners, population 2 is Toyota owners, and population 3 is Dodge owners. A sample was drawn from each population and each was asked whether he or she was satisfied with their car. Of 200 Honda owners, 180 were satisfied; of 300 Toyota owners, 260 were satisified; of 100 Dodge owners, 79 were satisfied. Test at α=0.10 whether the 3 population proportions who are satisfied are the same. Use the 5-step method. df = (2 rows-1)(3 cols-1) = 2. Fill out the graph fully, and compute the p-value. This is a one-tailed test. Compute the pvalue and show it on the graph. D. Test at α = 0.05 whether the two factors are independent. There are 4 car manufacturers, and each produces 3 sizes of car: small, medium, and large. If the factors are dependent, then buyers would tend to pick one of the manufacturers if they wanted small cars, and would tend to pick a different manufacturer if they wanted a larger car, and so on. If the factors (car make versus car size) are dependent, then we would reject Ho. Do the 5-step process (only STS exists) and fill out a graph. Compute the p-value and show it on the graph. A sample of 1000 purchasers gave the following information, which is the number of people who bought a certain size car from a certain manufacturer. Are the factors (car make versus size) independent? Small Medium Large Totals Honda 157 126 58 341 Toyota 65 82 45 192 Ford 181 142 60 383 Dodge 38 31 15 84 Totals 441 381 178 1000 df = (3 rows-1)(4 cols-1) = 6, and it is a one-tail test. [Note that we could have any number of rows and any number of columns when testing for independence.] ...
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