Statistics 350 – W09: Recommended Problems for HW 12 Textbook: Chapter 15, Exercises 15.9, 15.13, 15.14, 15.18, 15.27, 15.30, 15.31, 15.54 Chapter 17, Exercises 17.1, 17.2, 17.3, 17.5, 17.7, 17.8, 17.11 Additional Problems: #1 A market research study has investigated the relationship between a male adult’s self perception and his attitude toward small cars. A total of 299 males were surveyed at random. On their basis of responses, each was assigned to three personality types: 1. Cautious conservative 2. Middle of the roader 3. Confident explorer At the same time, each was asked about his overall opinion of small cars. The results are given below. Cautious conservative Middle of the roader Confident explorer Favorable 79 58 49 Neutral 10 8 9 Unfavorable 10 34 42 a. A 5% significance level will be used to determine whether these two traits (personality type and opinion of small cars) are independent. State the name of the test and the null hypotheses to be tested. b. The SPSS output is provided. Pick one of the expected counts and verify how it was found. Opinion of Small Cars * Personality Type Crosstabulation 79 58 49 186 61.6 62.2 62.2 186.0 10 8 9 27 8.9 9.0 9.0 27.0 10 34 42 86 28.5 28.8 28.8 86.0 99 100 100 299 99.0 100.0 100.0 299.0 Count Expected Count Count Expected Count Count Expected Count Count Expected Count Favorable Neutral Unfavorable Opinion of Small Cars Total Cautious conservative Middle of the roader Confident explorer Personality Type Total Chi-Square Tests 27.289 a 4 .000 30.327 4 .000 24.391 1 .000 299 Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases Value df Asymp. Sig. (2-sided) 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.94. a. c. Using the SPSS output above, give the value of the test statistic and the p-value. d. State your decision and conclusion in the context of this problem. #2 Records kept at a horse racetrack showed the following distribution of winners as a function of their starting position. All 144 races were run with a full field of eight horses. Starting Position 1 2 3 4 5 6 7 8 Number of Winners 32 21 19 20 16 11 14 11 Expected Counts a. A 5% significance level will be used to determine whether the starting position is associated with the probability of winning a race (i.e. if not associated, the probability of winning should be the same for any of the 8 starting positions). State the name of the test and the null hypotheses to be tested. b. Compute the expected counts (assuming H 0 is true). c. Compute the value of your test statistic. d. Use Table A.5 to give bounds for your p-value. e. What is the distribution of your test statistics if H 0 is true? Give all pertinent information. f. What is the expected value of your test statistic if H 0 is true? g. State your decision and conclusion in the context of this problem. #3 Read the Ten Guiding Principles on page 720-721 and pick one that is important to you and explain why. Kam Hamidieh Recommended Problems: