This is the second exam from Spring 1988 Unfortunately the take home exam that accompanied it is not available since the disk that contains it is unreadable by this version of Word 3 23 98 252y9822 ECO252 QBA2 Name SECOND HOUR EXAM Hour of Class Registered Circle February 18 1998 MWF 10 11 TR 12 30 2 00 Hour of Class Attended If Different I 14 points Do all the following x N 5 3 1 16 5 3 5 P 3 x 16 P z P 2 67 z 3 67 3 3 P 2 67 z 0 P 0 z 3 67 4962 4999 9961 2 3 5 0 5 P 0 x 3 P z z 0 67 P 167 3 3 P 167 z 0 P 0 67 z 0 4525 2486 2039 3 0 5 2 5 P 2 x 0 P z P 2 33 z 167 3 3 P 2 33 z 0 P 167 z 0 4901 4525 0376 4 0 5 P x 0 P z P z 167 3 P z 0 P 167 z 0 5000 4525 0475 5 2 5 F 2 The Cumulative probability P x 2 P z P z 100 3 P z 0 P 100 z 0 5000 3413 1587 6 A symmetrical interval about the mean with 82 probability We want two points x 09 and x 91 so that P x 91 x x 09 8200 From the diagram if we replace x by z P 0 z z 09 4100 The closest we can come is P 0 z 1 34 4099 So z 09 134 and x z 09 5 134 3 5 4 02 or 0 98 to 9 02 check 7 9 02 5 0 98 5 P 0 98 x 9 02 P z z 134 2 4099 8198 P 134 3 3 x 18 We want a point x 18 so that P x x 18 18 From the diagram if we replace x by z P 0 z z 18 32 The closest we can come is P 0 z 0 91 3186 or P 0 z 0 92 3212 Use something between the two So z 18 0 915 and x z 18 5 0 915 3 5 2 745 or 7 745 7 745 5 check P x 7 745 P z P z 0 92 P z 0 P 0 z 0 92 5000 3212 1788 3 2 3 20 98 252y9822 II 6 points 2 point penalty for not trying part a Show your work I wish to decide whether to become a high school teacher or a university professor I will do so on the basis of earnings alone I am interested in both a high salary and the certainty of getting it The data that I get in my sample is shown below Assume that the data represent independent samples taken from populations with the normal distribution x1 x2 d High School Teachers University Professors Difference 38 7 39 2 0 50 42 5 68 5 25 00 62 6 43 7 18 90 38 3 47 2 8 90 49 2 51 3 2 10 73 5 29 9 43 60 a Compute s1 the standard deviation for high school teachers 3 Note that x 2 46 63 s2 12 99 d 4 50 sd 23 86 You will not necessarily need all of these in your computations b Test to see if means for salaries of both types of teacher are equal You may assume that they come from populations with identical variances Does this indicate that one of the occupations is more lucrative 3 c Extra Credit Test to see if variances are equal What can you say about the relative safety of the two occupations 2 a Solution Item x1 304x 18 x1 1 38 7 50 80 n 6 2 s12 x12 1497 69 42 5 1806 25 2 16512 48 6 50 80 3 62 6 n 1 5 3918 76 s 14 343 205 728 1 4 38 3 1466 89 x 2 1 nx1 2 5 49 2 2420 64 6 73 5 5402 25 304 8 16512 48 Total b Solution From page 10 of the Syllabus Supplement Interval for Confidence Hypotheses Interval Difference H 0 0 d t 2 sd between Two H 1 0 1 1 Means sd s p 1 2 n1 n 2 unknown variances DF n1 n 2 2 assumed equal Test Ratio t s p2 d 0 sd Critical Value d cv 0 t 2 sd n1 1 s12 n2 1 s22 n1 n2 1 3 3 20 98 252y9822 H 0 0 H 0 1 2 H 1 0 Same as H 1 1 2 1 2 if 0 0 s p2 n1 1 s12 n2 1 s22 sd s p n1 n2 1 x1 511333 s12 197 835 d x1 x 2 4 50 5 205 728 5 12 78 10 2 x 2 46 63 s2 12 99 05 or as you specified DF n1 n2 2 6 6 2 10 205 728 163 3284 10 184 5542 t 025 2 228 2 1 1 1 1 s 184 5542 615181 7 8423 n1 n 2 6 6 Test Ratio t d 0 4 50 0 0 5737 This is between 2 228 sd 7 8433 or Critical Value d cv 0 t 2 sd 0 2 228 7 8433 17 75 d 4 50 is between these values or Confidence Interval d t 2 sd 4 50 2 228 7 8433 4 50 17 75 or 13 25 to 22 25 The interval includes 0 In all cases accept H 0 There is no difference in salaries c Solution From page 11 of the Syllabus Supplement Interval for Confidence Hypotheses Interval Ratio of Variances 2 2 H 2 2 F1 DF 21 DF2 1 1 DF2 F DF 2 2 s 0 1 2 1 DF2 22 F 5DF 2 2 5 2 2 H 1 1 2 1 s1 DF1 n1 1 DF2 n2 1 5 5 2 s2 205 728 5 5 F 12 1260 s2 12 78 2 There is no difference in risk 2 or 1 2 Test Ratio F DF1 DF2 Critical Value s12 s22 and F DF2 DF1 s22 s12 s2 1 5 5 5 5 F 22 Since both are below F 025 7 15 accept H 0 s1 1260 4 3 23 98 252y9822 III Do at least 2 of the following 4 Problems at least 10 each or do sections adding to at least 20 points Anything extra you do helps and grades wrap around Show your work State H 0 and H1 where applicable 1 In a random sample of 600 television sets made between Tuesday and Thursday from a production line 80 were defective In a random sample of 200 sets made on Monday 40 were defective a Using a 5 test test the hypothesis that the defect rate is larger on Monday than during the middle of the week 5 b If you conclude that the defect rate …
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