252y0631 11 28 06 Page layout view ECO252 QBA2 THIRD HOUR EXAM Nov 30 and Dec 1 2006 Name KEY Hour of Class Registered Circle MWF 1 MWF 2 TR 12 30 TR 2 I 8 points Do all the following 2points each unless noted otherwise Make Diagrams Show your work x N 15 9 3 20 15 P z 0 54 P z 0 P 0 z 0 54 1 P x 20 P z 9 3 5 2054 2946 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 54 Because this is on one side of zero we must subtract the area between 0 and 0 54 from the area above zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 15 Indicate the mean by a vertical line Shade the area above 20 This area is totally above the mean so we must subtract the area between the mean and 20 from the area 50 above the mean This is how we usually find a p value when the distribution of the test ratio is Normal 14 15 0 15 z P 1 61 z 0 11 2 P 0 x 14 P 9 3 9 3 P 1 61 z 0 P 0 11 z 0 4463 0438 4025 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 61 and 0 11 Because this is on one side of zero we must subtract the area between 0 11 and zero from the area between 1 61 and zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 15 Indicate the mean by a vertical line Shade the area between zero and 14 This area is totally below the mean so we must subtract the area between 14 and the mean 15 from the area between zero and the mean 16 15 16 15 z P 3 33 z 0 11 3 P 16 x 16 P 9 3 9 3 P 3 33 z 0 P 0 z 0 11 4996 0438 5434 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 33 and 0 11 Because this is on both sides of zero we must add together the area between 3 33 and zero and the area between zero and 0 11 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 15 Indicate the mean by a vertical line Shade the area between 16 and 16 This area includes the mean 15 and areas to either side of it so we add together these two areas 4 x 42 Find z 42 first Solution 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 42 is the value of z with 42 of the distribution above it Since 100 42 58 it is also the 58 th percentile Since 50 of the standardized Normal distribution is below zero your diagram should show that the probability between z 42 and zero is 58 50 8 or P 0 z z 42 0800 The closest we can come to this is P 0 z 0 20 0783 0 21 is also acceptable here So z 42 0 20 To get from z 42 to x 42 use the formula x z which x x 15 0 20 9 3 16 86 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 20 Show that 50 of the distribution is below the mean 7 If 42 of the distribution is above x 42 it must be above the mean and have 8 of the is the opposite of z 1 252y0631 11 28 06 Page layout view distribution between it and the mean Note that there will be some questions on the Final where you will need odd values of z like z 125 16 86 15 Check P x 16 86 P z P z 0 20 P z 0 P 0 z 0 20 9 3 5 0793 4207 42 2 252y0631 11 28 06 Page layout view II 22 points Do all the following 2points each unless noted otherwise Do not answer question yes or no without giving reasons Show your work in questions that are not multiple choice Look them over first The exam is normed on 50 points 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 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 3 Use a 5 significance level unless the question says otherwise 4 Read problems carefully A problem that looks like a problem on another exam may be quite different 5 Use statistical tests Just because two means or two proportions look different to you does not mean that they are significantly different unless you prove that the probability of getting the observed difference if the null hypothesis is true is very small 1 Turn in your computer problems 2 and 3 marked to show the following 5 points 2 point penalty for not doing a In computer problem 2 what is tested and what are the results b In computer problem 3 what coefficients are significant What is your evidence c In the last graph in computer problem 3 where is the regression line 5 2 Abronovic The distance that a baseball travels after being hit is a function of the velocity in mph of the pitched ball A ball is pitched to a batter with a 35 inch 32 oz bat that is swung at 70mph from the waist and at an angle of 35 The experiment is repeated 9 times A partial Minitab printout appears below Use 01 throughout this problem DIST Predictor Constant VELOC s 1 185 VELOC Coef StDev t ratio p 31 311 0 999 0 74667 0 01529 R sq Rsq adj Analysis of Variance SOURCE DF SS Regression 1 3345 1 Error 7 9 8 Total 8 3354 9 a MS 3345 1 1 4 F p The fastest pitchers can throw at about 100 mph How far will such a pitch be hit 2 b What is the value of R squared 2 c Fill in the F space in the ANOVA and explain specifically what is tested and what are the conclusions 3 d Is the constant 31 311 significant Why 2 14 Solution a The equation given above is Y b0 b1 X or DIST 31 311 …
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