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 31. P x 3 16 P z P z3 5316 532 67 3 67. . P z P z2 67 0 0 367 4962 4999 9961. . . . .2. P x0 3 P z P z0 533 53167 0 67. . P z P z167 0 0 67 0 4525 2486 2039. . . . .3. P x 2 0 P z P z2 530 532 33 167. . P z P z2 33 0 167 0 4901 4525 0376. . . . .4. P x 0 P z P z0 53167. P z P z0 167 0 5000 4525 0475. . . .5. F 2 (The Cumulative probability) P x 2 P z P z2 53100. P z P z0 100 0 5000 3413 1587. . . .6. A symmetrical interval about the mean with 82% probability.We want two points x x. .09 91 and , so that P x x x. ..91 098200 . From the diagram, if we replace x by z, P z z0 410009 ... The closest we can come is P z0 134 4099 . .. So z..09134, and x z .. .095 134 3 5 4 02, or 0.98 to 9.02.check: P x0 98 9 02. . P z P z0 98 539 02 53134 134. .. . 2 4099 8198. .7. x.18We want a point x.18, so that P x x ..1818. From the diagram, if we replacex by z, P z z0 3218 ... The closest we can come is P z0 0 91 3186 . . or P z0 0 92 3212 . .. Use something between the two. So z..180 915, and x z .. .185 0 915 3 5 2 745, or 7.745.check: P x 7 745. P z P z7 745 530 92.. P z P z0 0 0 92 5000 3212 1788. . . .23/20/98 252y9822II. (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 onthe 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.x1x2 dHigh School Teachers University Professors Difference38.7 39.2 0.5042.5 68.5 -25.0062.6 43.7 18.9038.3 47.2 -8.9049.2 51.3 -2.1073.5 29.9 43.60a. Compute s1, the standard deviation for high school teachers. (3) Note that x s2 246 63 12 99 . , .,d sd 4 50 2386. , .. 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 x12 1 38.7 1497.69 2 42.5 1806.25 3 62.6 3918.76 4 38.3 1466.89 5 49.2 2420.64 6 73.5 5402.25 Total 304.8 16512.48b. Solution: From page 10 of the Syllabus Supplement:Interval for Confidence IntervalHypotheses Test Ratio Critical ValueDifference between Two Means ( unknown, variances assumed equal) d t sd2s sn ndp 1 11 2DF n n 1 22HH :0:1 001 2tdsd0 sn s n sn np21 122 221 21 11 d t scvd 023 xxn11304 8650 80 .. sx nxn1212122116512 48 6 50 805. . 205 728.. s114 343 ..3/20/98 252y9822HH :01: 001 2Same as HH :if 01: 1 21 200 x sd x x1 121 2511333 197 8354 50 . , . ,. x sDF n n2 21 246 63 12 99052 6 6 2 10 . , ..or as you specified. sn s n sn np21 122 221 21 11 = 5 205 728 5 12 7810205 728 163 32842184 5542 2 228202510. .. .. .. ts sn ndp 1 11 2 . . .s 184 55421616615181 7 8423 Test Ratio: tdsd04 50 07 84330 5737... This is between 2 228..or Critical Value: d t scvd 02 0 2 228 7 8433 17 75. . . d 4 50. is between these values.or Confidence Interval: d t sd24 50 2 228 7 8433 4 50 17 75. . . . .or -13.25 to 22.25. The interval includes 0. In all cases accept H0. There is no difference in salaries.c. Solution: From page 11 of the Syllabus Supplement:Interval for Confidence IntervalHypotheses Test Ratio Critical ValueRatio of Variances FFDF DFDF DF121 221 21,, 212,5.5.21222122DFDFFssDF nDF n1 12 211 . .5 51222 orHH0 12221 1222:: FssDF DF1 21222, andFssDF DF2 12212, Fss5 51222 2205 72812 781260,... Fss5 5221211260,. . Since both are below F.,.0255 57 15, accept H0.There is no difference in risk.43/23/98 252y9822III. 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 H0 and H1where 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
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