252x0763 11/03/07Corrected ECO252 QBA2 Name SECOND EXAM Class________________________Nov 1-5 2007 Student Number_______________Show your work! Make Diagrams! Exam is normed on 50 points. Answers without reasons are not usually acceptable. 18,22~ Nx - If you are not using the supplement table, make sure that I know it.1. 1.200 xP2. 4242 xP 3. 24xP4. 045.x (Do not try to use the t table to get this.)252x0763 11/03/07II. (5+ points) Do all the following. Look them over first – There is a section III in the in-class exam and the computer problem is at the end. Show your work where appropriate. There is a penalty for not doing Problem 1a.Note the following:1. This test is normed on 50 points, but there are more points possible including the take-home. You are unlikely to finish the exam and might want to skip some questions.2. A table identifying methods for comparing 2 samples is at the end of the exam.3. If you answer ‘None of the above’ in any question, you should provide an alternative answer and explain why. You may receive credit for this even if you are wrong.4. Use a 5% significance level unless the question says otherwise.5. Read problems carefully. A problem that looks like a problem on another exam may be quite different. 6. Make sure that you state your null and alternative hypothesis, that I know what method you are using and what the conclusion is when you do a statistical test.1. (Groebner) We wish to compare the amount of time men and women spend in the supermarket. The two columns below, 1x and 2x represent two independent samples with 7 shoppers in each sample. You mayassume that the parent distributions are Normal. 21xxd Men Women DifferenceRow 1x 2x d 1 33 33 0 2 43 33 10 3 23 26 -3 4 29 41 -12 5 33 33 0 6 37 48 -11 7 26 44 -18Minitab computes the following.Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximumx1 7 32.00 2.55 6.76 23.00 26.00 33.00 37.00 43.00x2 7 36.86 2.91 7.69 26.00 33.00 33.00 44.00 48.00d 7 -4.86 -18.00 -12.00 -3.00 0.00 10.00a. Compute the sample variance for the d column – Show your work! (2)b. Is there a significant difference between the variances for men and women? State your hypotheses and your conclusion clearly! (2)c. Test to see there is a difference between the average amount of time men and women shop. (3)d. Using the sample means and standard deviations computed above and changing each sample size from 7 to 100, find a 91% 2-sided confidence interval for the difference between the amount of time men and women shop. Does it indicate a significant difference between men’s and women’s times? Why? (3) [10]252x0763 11/03/07III. (18+ points) Do as many of the following as you can. (2points each unless noted otherwise). Look them over first – the computer problem is at the end. Show your work where appropriate.Note that if you have a table like this 00.180.20.90.10., and if you know one number on theinside of the table, you can get the rest by subtracting.A professor wishes to see if the variability of scores for people taking the introductory accounting course is different. He takes a sample of the scores of 13 non-accounting students and 10 accounting students and gets the following results: ,131n ,102n 2.21021s and 5.3622s. Though this is a 2-sided test with a 95% confidence level, he can actually do the entire test by comparing a) 2221ss against 12,905.Fb) 2221ss against 12,9025.Fc) 2221ss against 9,1205.Fd) 2221ss against 9,12025.Fe) 2122ss against 12,905.Ff) 2122ss against 12,9025.Fg) 2122ss against 9,1205.Fh) 2122ss against 9,12025.F2. 9,1205.F_______ 150,25005.F is, at most, ______. If you did not get this from the Supplementary Tables, you must explain how you found this.252x0763 11/03/07Exhibit 1: Sample size Mean Std DeviationMarried 25 268.90 77.25Unmarried 30 455.10 102.40Standard error 24.2534Difference between means -186.206773.72534.2420.1860dsDd (Groebner et. al.) Bank managers want to find out if an incentive interest rate will cause more of an increase in spending by married cardholders than by unmarried cardholders. Let 1x represent the increase of spending by a random sample of 25 married cardholders and 2x represent increase of spending by a random sample of 30 unmarried cardholders. Sample data is above.3. If the bank finds that the difference between married and unmarried couples is 03.11020.186 .a. The difference is statistically significant because 186.20 is larger than 110.03b. The difference is statistically significant because the confidence interval supports a null hypothesis.c. The difference is statistically insignificant because 110.03 is smaller than 186.20.d. The difference is statistically insignificant because the confidence interval would lead us to reject a null hypothesis.4. If the researcher is trying to show that unmarried cardholders will increase their spending more than married cardholders, and, assuming that the population mean is appropriate to compare salaries,21D, her null hypothesis should be: a. 0Db. 0Dc. 0Dd. 0De. 0Df. 0Dg. None of the above5. If the researcher in exhibit 1 is attempting to show that unmarried cardholders will spend significantly more than married cardholders the appropriate critical value for the difference between the sample means is(assuming that zort is chosen correctly):a. 2534.240 zortb. 2534.240 zortc. 2534.240 zortd. 2534.2420.186 zorte. 2534.2420.186 zortf. 2534.2420.186 zort6. If the researcher does not believe that the population standard deviation for men and women are both the same, the appropriate degrees of freedom for the test (in problem 5) are:a. 53b. Gotten by the formula 1122122222121222121nnnsnsDFnsnsc. 25 (The smaller of 25 and 30)d. 55252x0763 11/03/07e. None of the above. (Use z instead of t.)7. I am testing the hypothesis 300:0H. I get a value of 162x, which results in a p-value of .076. What are the p-values for 300:0H and
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