DATA ANALYSIS 68 Assuming the heights of professional male tennis players follow a bell-shaped distribution, arrange in ascending order: I. A height with a z-score of 1. II. A height with a percentile rank of 80%. III. A height at the third quartile Q3. A. I, II, III B. I, III, II C. II, I, III D. III, I, II E. III, II, I DATA ANALYSIS 69 Suppose the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5, and a second student has a test result with a z-score of 2.0, how many points higher was the second student’s result than that of the first? A. 3.5 B. 4 C. 12 D. 16 E. 28 DATA ANALYSIS 70 Which of the following statements about influential points are true? I. Looking at a residual plot is an excellent way of picking out influential points. II. Removal of an influential point sharply affects the regression line. III. Determining a regression model with and without a point is an excellent way of picking out influential points. A. I and II B. I and III C. II and III D. I, II, and III E. None of the above gives the complete set of true responses. DATA ANALYSIS 71 Given this cumulative frequency plot, what can be said about the value of the mean? A. B. C. D. E. Between 10 and 15 Between 15 and 20 20 More than 20 From such a plot, one can determine the median, but nothing can be concluded about the mean. DATA ANALYSIS 72 Consider the points (-1,4), (2, 10), (4, 15), (7, 21), (10, n). What should n be so that the correlation between the x and y values is r =1 ? A. B. C. D. E. 26 27 28 A value different from any of the above. No value for n can make r =1. DATA ANALYSIS 73 A random sample of students from each of two schools was asked how many Supreme Court Justices they could name. The results are given in the two histograms: Which school has the greater median with regard to the number of Justices students could name, and which school has the greater mean? A. B. C. D. E. Greater median: A Greater median: A Greater median: B Greater median: B Greater median: B Greater mean: Greater mean: Greater mean: Greater mean: Equal means A B A B DATA ANALYSIS 74 Suppose that the scatterplot of log X and log Y shows a strong positive correlation close to 1. Which of the following is true? I. The variables X and Y will also have a correlation close to 1. II. A scatterplot of the variables X and Y will show a strong nonlinear pattern. III. The residual plot of the variables X and Y will show a random pattern. A. I only B. II only C. III only D. I and II E. I, II, and III DATA ANALYSIS 75 Which of the following are true statements? I. If the sample has variance zero, the variance of the population is also zero. II. If the population has variance zero, the variance of the sample is also zero. III. If the sample has variance zero, the sample mean and sample median are equal. A. I and II B. I and III C. II and III D. I, II, and III E. None of the above gives the complete set of true responses. DATA ANALYSIS 76 Consider the three correlations depicted below. Which of the statements on the following slide gives a proper ordering? A. B. C. D. E. r₁ < r₃ < r₂ r₂ < r₃ < r₁ r₂ < r₁ < r₃ < |r₂| r₃ < r₁ < |r₂| r₁ < r₂ < r₃ < |r₂| DATA ANALYSIS 77 Four pairs of data are used in determining a regression line y = -2 + 6x. If the four values of the independent variable are 37, 52, 18, and 23, respectively, what is the mean of the four values of the dependent variable? A. 32.5 B. 193 C. 195 D. 778 E. The mean cannot be determined from the given information. DATA ANALYSIS 78 When there are multiple gaps and clusters, which of the following is the best choice to give an overall picture of a distribution? A. Mean and standard deviation B. Median and interquartile range C. Boxplot and its five-number summary D. Stemplot or histogram E. None of the above are really helpful in showing gaps and clusters. DATA ANALYSIS 79 A study of marital status of adults in the United States results in the following segmented bar chart: Which of the following is greatest? A. Number of adults in 1900 who were married. B. One half the number of adults in 1950 who were married. C. Number of adults in 2000 who were widowed, divorced, or never married. D. The above all are equal. E. It is impossible to determine the answer without knowing the actual numbers of people involved. DATA ANALYSIS 80 If quartiles Q1 = 50 and Q3 = 70, which of the following must be true? I. The median is 60. II. The mean is between 50 and 70. III. The standard deviation is at most 20. A. I only B. II only E. None may be true. C. III only D. All are true.