252y0721 3 19 07 ECO252 QBA2 SECOND HOUR EXAM March 23 2007 Name KEY 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 Make diagrams x N 10 7 If you are not using the supplement table make sure that I know it 25 10 7 10 z 1 P 7 x 25 P P 0 43 z 2 14 7 7 P 0 43 z 0 P 0 z 2 14 1664 4838 6502 For z make a diagram Draw a Normal curve with a mean at 0 Indicate the mean by a vertical line Shade the area between 0 43 and 2 14 Because this is on both sides of zero we must add together the area between 0 43 and zero and the area between zero and 2 14 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 10 Indicate the mean by a vertical line Shade the area between 7 and 25 This area includes the mean 10 and areas to either side of it so we add together these two areas 15 10 P z 0 71 P z 0 P 0 z 0 71 5 2611 2 P x 15 P z 7 2389 For z make a diagram Draw a Normal curve with a mean at 0 Indicate the mean by a vertical line Shade the area above 0 71 Because this is on one side of zero we must take the area above zero and subtract the area between zero and 0 71 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 10 Indicate the mean by a vertical line Shade the area above 15 Since 15 is to the right of the mean 10 this area will be totally to the right of the mean Because this area is entirely to the right we must subtract the area between the mean and 15 from the entire area above the mean 0 10 5 10 z P 2 14 z 1 43 3 P 5 x 0 P 7 7 P 2 14 z 0 P 1 43 z 0 4838 4236 0602 For z make a diagram Draw a Normal curve with a mean at 0 Indicate the mean by a vertical line Shade the area between 2 14 and 1 43 Because this is on one side of zero we must take the area between 2 14 and zero and subtract the area between 1 43 and zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 10 Indicate the mean by a vertical line Shade the area between 5 and zero Both 5 and zero are below the mean 10 The area is to the left of the mean and we must subtract the smaller of the two areas between zero and 10 from the larger area between 5 and 10 x 085 Do not try to use the t table to get this For z make a diagram Draw a Normal curve with a mean at 0 z 085 is the value of z with 8 5 of the distribution above it Since 100 8 5 91 5 it is 4 also the 91 5th percentile Since 50 of the standardized Normal distribution is below zero your diagram should show that the probability between z 085 and zero is 91 5 50 41 5 or P 0 z z 085 4150 The closest we can come to this is P 0 z 1 37 4147 1 38 is also acceptable here So z 085 1 37 To get from z 085 to x 085 use the formula x z 1 252y0721 3 19 07 x x 10 1 37 7 19 59 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 10 Show that 50 of the distribution is below the mean 10 If 8 5 of the distribution is above x 085 it must be above the mean and have 41 5 of the distribution between it and the mean 19 59 10 Check P x 19 59 P z P z 1 37 P z 0 P 0 z 1 37 7 5 4147 08530 8 5 which is the opposite of z 2 252y0721 3 19 07 II 22 points Do all the following 2points each unless noted otherwise Look them over first the computer problem is at the end Show your work where appropriate 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 Anderson Sweeny Williams We wish to compare miles per gallon of two similar automobiles A random sample of 8 automobiles is chosen and 8 drivers are asked to drive the cars on identical roads The data is as follows Row Driver Model 1 Model 2 x1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 difference x2 28 23 25 23 24 26 29 24 d 26 22 27 22 23 25 27 26 2 1 2 1 1 1 2 2 I have computed x1 25 25 s1 2 2520 x 2 24 75 and s 2 2 1213 a Compute the sample variance for the d column Show your work 2 Solution If you are using the computational method compute columns 1 and 2 below If time is not important to you and you are using the definitional method compute columns 1 3 and 4 below Column 1 2 3 4 2 Row d d d d 2 So n 8 d 4 d 20 2 d d 1 2 3 4 5 6 7 8 First d s 2 d n x 2 nx 2 n 1 d d n 1 2 1 2 1 1 1 2 2 4 2 4 1 4 1 1 1 4 4 20 1 5 0 5 2 5 0 5 0 5 0 5 1 5 2 5 0 0 2 25 0 25 6 25 0 25 0 25 0 25 2 25 6 25 18 00 d d 0 and 2 d d 18 00 4 x1 x 2 25 25 24 75 0 5 The …
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