252x0763 11 03 07 Corrected ECO252 QBA2 SECOND EXAM Nov 1 5 2007 Name Class Student Number Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable x N 22 18 If you are not using the supplement table make sure that I know it 1 P 0 x 20 1 2 P 42 x 42 3 P x 24 4 x 045 Do not try to use the t table to get this 252x0763 11 03 07 II 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 x1 and x 2 represent two independent samples with 7 shoppers in each sample You may assume that the parent distributions are Normal d x1 x 2 Men x1 Row 1 2 3 4 5 6 7 Women 33 43 23 29 33 37 26 x2 Difference d 33 33 26 41 33 48 44 0 10 3 12 0 11 18 Minitab computes the following Variable x1 x2 d N 7 7 7 Mean 32 00 36 86 4 86 SE Mean 2 55 2 91 StDev 6 76 7 69 Minimum 23 00 26 00 18 00 Q1 26 00 33 00 12 00 Median 33 00 33 00 3 00 Q3 37 00 44 00 0 00 Maximum 43 00 48 00 10 00 a 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 07 III 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 10 90 and if you know one number on the 20 80 1 00 inside of the table you can get the rest by subtracting Note that if you have a table like this 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 n1 13 n 2 10 s12 210 2 and s 22 36 5 Though this is a 2 sided test with a 95 confidence level he can actually do the entire test by comparing a b c d e f g h s12 s 22 s12 s 22 s12 s 22 s12 s 22 s 22 s12 s 22 s12 s 22 s12 s 22 s12 9 12 against F 05 9 12 against F 025 12 9 against F 05 12 9 against F 025 9 12 against F 05 9 12 against F 025 12 9 against F 05 12 9 against F 025 12 9 2 F 05 250 150 F 05 is at most If you did not get this from the Supplementary Tables you must explain how you found this 252x0763 11 03 07 Exhibit 1 Sample size Married 25 Unmarried 30 Standard error 24 2534 Mean Std Deviation 268 90 77 25 455 10 102 40 d D0 186 20 7 6773 sd 24 2534 Difference between means 186 20 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 x1 represent the increase of spending by a random sample of 25 married cardholders and x 2 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 186 20 110 03 a The difference is statistically significant because 186 20 is larger than 110 03 b 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 D 1 2 her null hypothesis should be a D 0 b D 0 c D 0 d D 0 e D 0 f D 0 g None of the above 5 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 t or z is chosen correctly a 0 t or z 24 2534 b 0 t or z 24 2534 c 0 t or z 24 2534 d 186 20 t or z 24 2534 e 186 20 t or z 24 2534 f 186 20 t or z 24 2534 6 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 53 b Gotten by the formula s12 s22 n n2 1 DF 2 2 s12 n1 n1 1 c 25 The smaller of 25 and 30 d 55 s 22 2 n2 n2 1 252x0763 11 03 07 e None of the above Use z instead of t 7 I am testing the hypothesis H 0 300 I get a value of x 162 which results in …
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