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Cumulative Review Problems
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1 Explain the difference between a statistic and a parameter 2 TRUE FALSE The area under a normal curve between z = 01 and z = 05 is the same as the area between z = 03 and z = 07 3 The following scores were achieved by students on a statistics test: 82, 93, 26, 56, 75, 73, 80, 61, 79, 90, 94, 93, 100, 71, 100, 60 Compute the mean and median for these data and explain why they are different 4 Is it possible for the standard deviation of a set of data to be negative Zero Explain 5 For the test scores of problem #3, compute the five-number summary and draw a boxplot of the data
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116 U Step 4 Review the Knowledge You Need to Score High
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Solutions to Practice Problems
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Multiple Choice
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1 The correct answer is (d) b = r sy 075 = (055) = 026 16 sx
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2 The correct answer is (e) The value of a residual = actual value predicted value = 25 [235 + 086(29)] = 229 3 The correct answer is (a) r 2 = ( 058)2 = 03364 This is the coefficient of determination, which is the proportion of the variation in the response variable that is explained by the regression on the independent variable Thus, about one-third (333%) of the variation in hours spent exercising can be explained by hours spent watching television (b) is incorrect since correlation does not imply causation (c) would be correct if b = 058, but there is no obvious way to predict the response value from the explanatory value just by knowing r (d) is incorrect for the same reason (b) is incorrect (e) is incorrect since r, not r 2, is given In this case r 2 = 03364, which makes (a) correct 4 The correct answer is (c) ln( y) = 164 088(31) = 1088 y = e 1088 = 0337 5 The correct answer is (c) The pattern is more or less random about 0, which indicates that a line would be a good model for the data If the data are linearly related, we would expect them to have a non-zero correlation 6 The correct answer is (b) I is incorrect the predicted weight of a person 61 inches tall is 1046 pounds II is a correct interpretation of the slope of the regression line (you could also say that For each additional inch of Height, Weight is predicted to increase by 36 pounds) III is incorrect It may well be true, but we have no way of knowing that from the information given 7 The correct answer is (c) The predicted score for the student is 2735 + (912)(3) = 5471 The residual is the actual score minus the predicted score, which equals 510 5471 = 371 8 The correct answer is (b) Consider the expression for r r = x x 1 s n 1 x y y s y
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Adding 12 to each Y-value would not change sy Although the average would be 12 larger, the differences y y would stay the same since each Y-value is also 12 larger By taking the negative of each X-value, each term x x would reverse sign (the mean also reverses sx
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sign) but the absolute value of each term would be the same The net effect is to leave unchanged the absolute value of r but to reverse the sign 9 The correct answer is (e) The question is asking for the coefficient of determination, r 2 (R-sq on many computer printouts) In this case, r = 08877 and r 2 = 07881, or 788% This can be found on your calculator by entering the GPA scores in L1, the SAT scores in L2, and doing STAT CALC 1-Var Stats L1,L2
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