Explain the difference between a statistic and a parameter.
- True–False. The area under a normal curve between z = 0.1 and z = 0.5 is the same as the area
between z = 0.3 and z = 0.7. - 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. - Is it possible for the standard deviation of a set of data to be negative? Zero? Explain.
- For the test scores of problem #3, compute the five-number summary and draw a boxplot of the data.
Solutions to Practice Problems
Multiple-Choice
The correct answer is (d).
- The correct answer is (e). The value of a residual = actual value – predicted value = 25 – [2.35 +
0.86(29)] = –2.29. - The correct answer is (a). r 2 = (-0.58)^2 = 0.3364. 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 (33.3%) 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 = –0.58, 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 = 0.3364, which makes (a) correct. - The correct answer is (c). ln (y ) = 1.64 – 0.88(3.1) = –1.088 y = e –1.088 = 0.337.
- 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. - The correct answer is (b). I is incorrect—the predicted weight of a person 61 inches tall is 104.6
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 3.6 pounds).” III is incorrect. It may
well be true, but we have no way of knowing that from the information given. - The correct answer is (c). The predicted score for the student is 273.5 + (91.2)(3) = 547.1. The
residual is the actual score minus the predicted score, which equals 510 – 547.1 = –37.1. - The correct answer is (b). Consider the expression for r . .
Adding 12 to each Y -value would not change s (^) y . Although the average would be 12 larger, the