252y0551 10 31 05 Open in Print Layout format ECO252 QBA2 FIRST HOUR EXAM October 17 18 2005 Name Key Hour of class registered Class attended if different Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable I 8 points Do all the following If you do not use the standard Normal table explain x N 2 5 6 For z Make diagrams For x draw a Normal curve with a vertical line in the center at 2 5 draw a Normal curve with a vertical line in the center at zero 3 2 5 19 5 2 5 z P 3 67 z 0 08 1 P 19 5 x 3 P 6 6 P 3 67 z 0 P 0 z 0 08 4999 0319 5318 1 252y0551 10 31 05 Open in Print Layout format 2 5 2 5 0 2 5 z 2 P 0 x 2 50 P P 0 42 z 0 1628 6 6 10 22 2 5 3 P x 10 22 P z P z 1 29 6 P z 0 P 0 z 1 29 5 4015 0985 2 252y0551 10 31 05 Open in Print Layout format 4 x 06 There is no excuse for not being able to do this at this point since you should have done it 3 times in the take home To find z 06 make a Normal diagram for z showing a mean at 0 and 50 above 0 divided into 6 above z 06 and 44 below z 04 So P 0 z z 06 4400 The closest we can come is P 0 z 1 55 4394 or P 0 z 1 56 4406 So use z 06 1 555 x 06 z 06 2 5 1 555 6 11 83 For the method of creating the diagrams go to 252y0551s 3 252y0551 10 31 05 Open in Print Layout format II 5 points 2 point penalty for not trying part a A dealer wishes to test the manufacture s claim that the Toyota Caramba gets 28 miles per gallon The data below is found Recomputing what I ve done for you is a great way to waste time a Compute the sample standard deviation s of the miles per gallon Show your work 2 b Is the population mean significantly different using a 95 confidence level from 28 mpg Show your work 3 c Extra Credit Find an approximate p value for your null hypothesis 2 Solution a Compute the sample Row x x2 standard deviation s of the miles per 1 28 82 830 592 gallon Show your work 2 2 23 71 562 164 3 29 25 855 563 x 264 02 x 26 402 4 25 16 633 026 n 10 5 27 60 761 760 x 2 nx 2 6 27 41 751 308 7018 253 10 26 402 2 2 s 7 27 23 741 473 n 1 9 8 26 42 698 016 47 59696 9 21 75 473 063 5 28855 9 10 26 67 711 289 sum 264 02 7018 253 s 5 28855 2 299685 Note that excessive rounding can throw this answer way off Using x 26 I got s2 7018 10 26 2 7018 6760 258 28 667 and s 5 3541 9 9 9 b Is the population mean significantly different using a 95 confidence level from 28 mpg Show your work 3 Given x 26 402 s 2 2997 n 7 and 05 DF n 1 9 and 9 t 025 2 262 We are testing H 0 28 Use only one of the following Confidence Interval s x s n 2 2997 10 5 28855 0 52855 0 7272 10 x t 2 s x 26 402 2 262 0 7272 26 402 1 6449 or 24 757 to 28 047 Since 28 is on the confidence interval it is not significantly different from the sample mean s 2 2997 5 28855 0 52855 0 7272 Critical Value s x 10 n 10 x cv t 2 s x 28 2 262 0 7272 28 1 6449 or 26 36 to 29 65 Since 26 402 is between the critical values it is not significantly different from the population mean Test Ratio s x s n 2 2997 10 5 28855 0 52855 0 7272 10 x 0 26 402 28 t 2 197 The accept zone is between 2 262 and 2 262 Since sx 0 7272 2 197 is between these values do not reject the null hypothesis c Extra Credit Find an approximate p value for your null hypothesis 2 9 9 2 197 is between t 025 2 262 and t 05 1 833 Since pval 2 P t 2 197 it is between 05 and 10 4 252y0551 10 31 05 Open in Print Layout format For Minitab computation of variance and hypothesis test go to 252y0551s 5 252y0551 10 31 05 Open in Print Layout format III Do all of the following problems 2 each unless marked otherwise adding to 18 points Show your work except in multiple choice questions Actually it doesn t hurt there either If the answer is None of the above put in the correct answer 1 For sample sizes less than 10 the sampling distribution of the mean will be approximately normally distributed a Regardless of the shape of the population b Only if the shape of the population is symmetrical c Only if the standard deviation of the samples are known d Only if the sample is normally distributed 2 The width of a confidence interval estimate for a proportion will be a Narrower for 99 confidence than for 95 confidence b Wider for a sample size of 100 than for a sample size of 50 c Narrower for 90 confidence than for 95 confidence d Narrower when the sample proportion is 0 50 than when the sample proportion is 0 20 3 Which of the following would be an appropriate null hypothesis a The mean of a population is equal to 55 b The mean of a sample is equal to 55 1 The mean of a population is greater than 55 2 Only a and c are true 4 A Type II error is committed when a We reject a null hypothesis that is true b We don t reject a null hypothesis that is true Note that b and c are not errors c We reject a null hypothesis that is false d We don t reject a null hypothesis that is false 5 If we are performing a two tailed test of whether 100 the power of the test in detecting a shift of the mean to 105 will be its power detecting a shift of the mean to 94 a Less than 94 is further from 100 than 105 b Greater than c Equal to 3 Not comparable to 10 6 From a sample of 100 students we find that the mean expenditure for books is 316 40 with a standard deviation of 43 20 You are asked to test …
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