Note:The enclosed exam solutions are for exam 252x9851 which was given two weeks later than your first exam. The questions apply to your exams as follows:I Exam 1 (and 2)II Exam 1 (and 2)III 1. Exam 1 2. Exam 2 3a-d Exam 1 3e Exam 2 4. Exam 1 5. Exam 2 6. Exam 1Computer Problem Exam 2252y9851 continues in document 252z9851Exam starts on next page.10/23/98 252y9851 ECO252 QBA2 Name FIRST HOUR EXAM October 17, 1998Show your work! I. (14 points) Do all the following. 8,5.1~ Nx1. P x1 30 56.306.085.13085.11 zPzP 5237.4998.0239.56.30006.0 zPzP2. 55 xP 44.081.085.1585.15 zPzP 4610.1700.2910.44.00081.0 zPzP3. 93 xP 94.019.085.1985.13 zPzP 2511.0753.3264.19.0094.00 zPzP4. 0xP 19.085.10 zPzP 5753.5000.0753.0019.0 zPzP5. 5.10.7 xP 3554.006.185.15.185.17 zPzP6. A symmetrical interval about the mean with 63% probability.We want two points 8150.1850. and xx, so that 6300.8150.1850. xxxP. From the diagram, if we replace x by z, 3150.01850. zzP. The closest we can come is 3159.90.00 zP. So 90.01850.z, and 2.75.1890.05.11850.zx, or –5.7 to 8.7.7. 045.xWe want a point 045.x, so that 045.045.xxP. From the diagram, if we replace x by z, 455.0045. zzP. The closest we can come is 4554.70.10 zP. So 70.1045.z, and 6.135.1870.15.1045.zx, or 15.1 .210/23/98 252y9851II. (6 points-2 point penalty for not trying part a.) Show your work! Samples of five automobiles from one manufacturer and six automobiles from a second manufacturer were tested for top speeds. These are listed below. Assume that we were sampling from a normal distribution. Manufacturer 1 Manufacturer 2Automobile Speed Automobile Speed 1 110 1 115 2 135 2 130 3 125 3 140 4 185 4 190 5 130 5 135 6 142Note that 4165.25,14222 sxa. Compute the sample variance, 1s, of the top speed of automobiles for the first manufacturer. Show your work.(3)Solution:Manufacturer x (Speed) x2 1 110 12100 2 135 18225 3 125 15625 4 185 34225 5 130 16900 Total 685 97075. b. Compute a 99% confidence interval for the mean top speed, 1, of automobiles for the first manufacturer.(3)Solution: From the problem statement .01. From page 10 of the syllabus supplement, if the population variance is unknown x t sx2 and 604.44005.12ttn.7083.1254165.2855.80711nssx. So 51.581377083.12604.41371 or 76.49 to 195.51.3 13756851nxx 41375970751221221nxnxs 5.807 or 4165.281s.10/23/98 252y9851III. Do at least 3 of the following 6 Problems (at least 10 each) (or do sections adding to at least 30 points - Anything extra you do helps, and grades wrap around) . Show your work!1. Using the data from the previous problem (page 2.), test the hypothesis that the population mean, 1, for the first manufacturer is 135 at the 99% confidence level using:a. A test ratio (2)b. Critical values (2)c. A confidence interval (2)d. Find an approximate p-value for the null hypothesis. (1)e. Now find a 95% confidence interval for the standard deviation.(3)Solution: From page 10 of the Syllabus Supplement:Interval for Confidence IntervalHypotheses Test Ratio Critical ValueMean ( known) x zx2HH0 01 0:: zxx0x zcv x 02Mean ( unknown) x t sx2DF n 1HH0:: 01 0txsx0x t scv x 02135:H135:H10 604.4,01.,41,1354005.1210ttnDFnFrom the previous page: 1371x and 7083.1254165.2855.80711nssx.a. Test Ratio: 1574.07083.12135137110xsxt. This is in the 'accept region'between -4.604 and +4.604, so accept H0.b. Critical Value: 1102xcvstx 51.581357083.12604.4135 or 76.5 to 193.5. This includes 1371x, so accept H0.c. Confidence Interval: 1112xstx 51.581377083.12604.4137 or 78.5 to 195.5. This includes 13510, so accept H0.d. From the t table t= 0.1574 is smaller than 134.0445.t, so that, if this were a 1-sided test, we couldsay 45pvalue. Since this is a 2-sided test, we double p-value, and say 90pvalue.e. From page 1 of the Syllabus Supplement: n s n s 1 122222122 .41 nDF and 05.. Since 025.2 and 975.21 , look up 42025. and 42975.. So 2975.21212025.2111snsn or 2158.05.80741433.115.807421 or 56.1496786.28921. Finally, taking square roots, 342.122025.171.410/23/98 252y98512. Repeating the data from the previous problem: Manufacturer 1 Manufacturer 2Automobile Speed Automobile Speed 1 110 1 115 2 135 2 130 3 125 3 140 4 185 4 190 5 130 5 135 6 142Note that 4165.25,14222 sxTest the hypothesis that cars produced by the second manufacturer have higher top speeds than those produced by the first manufacturer by comparing means using:a. A test ratio (3)b. Critical values (2)c. A confidence interval (2)d. Find an approximate p-value for the null hypothesis. (1)e. Now find a 95% confidence interval for the ratio, 21, of standard deviations.(3)Note: You may assume either (i) that population variances are the same for the two parent populations or (ii) that they are not equal, but if you assume that they are not equal part a) is 5 points and b) and c) are 3 points each. So, indicate what you assume.f. Do a test to see if
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