252y0721 3/19/07 ECO252 QBA2 Name KEY SECOND HOUR EXAMMarch 23 2007Show 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! 7,10~ Nx - If you are not using the supplement table, make sure that I know it.1. 257 xP 14.243.0710257107 zPzP 14.20043.0 zPzP6502.4838.1664. 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. 2. 15xP 71.071015 zPzP 71.000 zPzP2611.5. =.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 entirelyto the right we must subtract the area between the mean and 15 from the entire area above the mean. 3. 05 xP 43.114.271007105 zPzP 043.1014.2 zPzP0602.4236.4838. 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).4. 085.x (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. 085.z is the value of z with 8.5% of the distribution above it. Since 100 – 8.5 = 91.5, it is also the 91.5th percentile. Since 50% of the standardized Normal distribution is below zero, your diagram should show that the probability between 085.z and zero is 91.5% - 50% = 41.5% or .4150.0085. zzP The closest we can come to this is .4147.37.10 zP (1.38 is also acceptable here.) So .37.1085.z To get from 085.z to 085.x, use the formula zx , 1252y0721 3/19/07which is the opposite of xz . 59.19737.110 x. 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 085.x, it must be above the mean and have 41.5% of the distribution between it and the mean.Check: 59.19xP 37.171059.19 zPzP 37.100 zPzP%5.808530.4147.5. .2252y0721 3/19/07II. (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 difference 1x 2x d 1 1 28 26 2 2 2 23 22 1 3 3 25 27 -2 4 4 23 22 1 5 5 24 23 1 6 6 26 25 1 7 7 29 27 2 8 8 24 26 -2I have computed 25.251x, 2520.21s, 75.242x and 1213.22sa. 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) Row d 2d dd 2dd 1 2 4 1.5 2.25 2 1 1 0.5 0.25 3 -2 4 -2.5 6.25 4 1 1 0.5 0.25 5 1 1 0.5 0.25 6 1 1 0.5 0.25 7 2 4 1.5 2.25 8 -2 4 -2.5 6.25 4 20 0.0 18.00So 8n, 4d, 202d, 0ddand 00.182dd.First 5.075.2425.258421xxndd. The formula for the sample variance is1222nxnxs. For the difference this becomes 1222ndndsd 75.08202 5714.2700.1812ndd. 6036.1ds3252y0721 3/19/07b. Is there a significant difference between the gas
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