252y0762 10 30 07 ECO252 QBA2 SECOND EXAM Nov 1 5 2007 Name KEY Class Student Number Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable x N 12 9 If you are not using the supplement table make sure that I know it 21 12 21 12 z P 3 67 z 1 00 1 P 21 x 21 P 9 9 P 3 67 z 0 P 0 z 1 00 4999 3413 8412 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 3 67 and 1 00 Because this is on one side of zero we must add the area between 3 67 and zero to the area between zero and 1 00 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 12 Indicate the mean by a vertical line Shade the area between 21 and 21 This area is on both sides of the mean 12 so we add to get our answer 14 12 P z 0 22 2 P x 14 P z 9 P z 0 P 0 z 0 22 5 0871 4129 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 22 Because this is on one side of zero we must subtract the area between zero and 0 22 from the area above zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 12 Indicate the mean by a vertical line Shade the above 14 This area is on one side of the mean 12 so we subtract to get our answer 10 05 12 0 12 z 3 P 0 x 10 05 P P 1 33 z 0 22 9 9 P 1 33 z 0 P 0 22 z 0 4082 0871 3211 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 1 33 and 0 22 Because this is on one side of zero we must subtract the area between 0 22 and zero from the larger area between 0 22 and zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 12 Indicate the mean by a vertical line Shade the area between zero and 10 05 This area is on one side of the mean 12 so we subtract to get our answer x 055 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 055 is the value of z with 5 5 of the distribution above it Since 100 5 5 94 5 it is 4 also the 94 5th percentile Since 50 of the standardized Normal distribution is below zero your diagram should show that the probability between z 055 and zero is 94 5 50 44 5 or P 0 z z 055 4450 The closest we can come to this is P 0 z 1 60 4452 1 59 is also acceptable here So z 055 1 60 To get from z 055 to x 055 use the formula x z which is x x 12 1 60 9 26 40 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 12 Show that 50 of the distribution is below the mean 12 If 5 5 of the distribution is above x 055 it must be above the mean and have 44 5 of the distribution between it and the mean the opposite of z 252y0762 10 30 07 26 40 12 Check P x 26 40 P z 9 P z 1 60 P z 0 P 0 z 1 60 5 4452 0548 055 252y0762 10 30 07 II 5 points Do all the following Look them over first There is a section III in the in class exam and the computer problem is at the end Show your work where appropriate There is a penalty for not doing Problem 1a 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 Groebner We wish to compare the amount of time men and women spend in the supermarket The two columns below x1 and x 2 represent two independent samples with 7 shoppers in each sample You may assume that the parent distributions are Normal d x1 x 2 Men x1 Row 1 2 3 4 5 6 7 Women 32 42 22 28 32 36 25 x2 Difference d 33 33 26 41 33 48 44 1 9 4 13 1 12 19 Minitab computes the following Variable x1 x2 d N 7 7 7 Mean 31 00 36 86 5 86 SE Mean 2 55 2 91 StDev 6 76 7 69 Minimum 22 00 26 00 19 00 Q1 25 00 33 00 13 00 Median 32 00 33 00 4 00 Q3 36 00 44 00 1 00 Maximum 42 00 48 00 9 00 a Compute the sample variance for the d column Show your work 2 b Is there a significant difference between the variances for men and women State your hypotheses and your conclusion clearly 2 c Test to see there is a difference between the average amount of time men and women shop 3 d Using the sample means and standard deviations computed above and changing each sample size from 7 to 100 find an 89 2 sided confidence interval for the difference between the amount of time men and women shop Does it indicate a significant difference between men s and women s times Why 3 10 Solution a Compute the sample variance for the d column Show your work 2 7 20 400 Row d d2 1 2 3 4 5 6 2 8 5 14 2 13 4 64 25 196 4 169 48 862 So n 7 First d 48 d d d n 2 862 48 6 85714 x1 x 2 31 00 36 86 5 7 252y0762 10 30 07 The formula for …
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