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DATA ANALYSIS 53 Given the two histograms below, which of the following statements are true? Slide 2 I. The Empirical Rule applies only to set A. II. You can be sure that the standard deviation of set A is greater than 5. III. You can be sure that the standard deviation of set B is greater than 5. A. I only B. II only C. I and II D. I and III E. II and III Slide 3 Slide 4 DATA ANALYSIS 54 A data set includes two outliers, one at each end. If both these outliers are removed, which of the following is a possible result? A. Both the mean and standard deviation remain unchanged. B. Both the median and standard deviation remain unchanged. C. Both the standard deviation and variance remain unchanged. D. Both the mean and median remain unchanged. E. Both the mean and standard deviation increase. Slide 5 Slide 6 DATA ANALYSIS 55 The following is a histogram of test scores. Which of the statements on the following slide are true? Slide 7 I.The median score was 75. II.If 90 and above was an A, most students received an A. III.More students scored below 70 than above 90. A. I only B. II only C. III only D. All are true. E. None are true. Slide 8 Slide 9 DATA ANALYSIS 56 A linear regression analysis is performed on the data from two scatterplots, A and B, resulting in identical least squares regression lines with positive slopes. Which of the statements on the following slide is true? Slide 10 A. The sum of the squares of the residuals in A equals the sum of the squares of the residuals in B. B. The correlation in A equals the correlation in B. C. If the sum of the squares of the residuals in A is greater than the sum of the squares of the residuals in B, than the correlation in A will be greater than the correlation in B. D. If the sum of the squares of the residuals in A is greater than the sum of the squares of the residuals B, then the correlation in A will be less than the correlation in B. E. None of the above are true statements. Slide 11 Slide 12 DATA ANALYSIS 57 Consider n pairs of numbers. Suppose x-bar = 4, s x = 3, y-bar = 2, and s y = 5. Of the following which could be the least squares line? A. y = 2 + x B. y = -6 +2x C. y = -10 + 3x D. y = 5/3 x E. y = 6 - x Slide 13 Slide 14 DATA ANALYSIS 58 A histogram of the educational level (in number of years of schooling) of the adult populations of the United States would have which of the following characteristics? I.Symmetry II.Clusters III.Skewness to the left A. II only B. I and II C. I and III D. II and III E. I, II, and III Slide 15 Slide 16 DATA ANALYSIS 59 A doctor wishes to compare the resting heart rates of his younger patients (younger than 30 years old) versis his older patients (older than 30 years old). Which of the following graphical displays is inappropriate? A. back-to-back stemplot B. Parallel boxplots C. Side by side histograms D. Scatterplot E. All the above displays are inappropriate. Slide 17 Slide 18 DATA ANALYSIS 60 Which of the following are true statements about the correlation coefficient r ? I.It is not affected by changes in the measurement units of the variables. II.It is not affected by which variable is called x and which is called y. III.It is not affected by extreme values. 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. Slide 19 Slide 20 DATA ANALYSIS 61 Which of the following measures are most usually given to describe the center and spread of a distribution as given in the dotplot? Slide 21 A. Mean and standard deviation B. Mean and interquartile range C. Mean and range D. Median and interquartile range E. Median and range Slide 22 Slide 23 DATA ANALYSIS 62 Suppose the correlation between two variables is 0.85. If each of the y-values is multiplied by -1, which of the following is true about the new scatterplot? A. It slopes up to the right, and the correlation is -0.85. B. It slopes down to the right, and the correlation is -0.85. C. It slopes up to the right, and the correlation is 0.85. D. It slopes down to the right, and the correlation is 0.85. E. None of the above is true. Slide 24 Slide 25 DATA ANALYSIS 63 Which of the following distributions has a mean of 60 and a standard deviation of 4 ? Slide 26 Slide 27 DATA ANALYSIS 64 Suppose X and Y are random variables with = 38, = 12, = 35, and = 9. Given that X and Y are independent, what is the standard deviation of the random variable X-Y ? A. 3B. 21C. 3D. 15E. 21 Slide 28 Slide 29 DATA ANALYSIS 65 Which of the following statements are true? I.All symmetric histograms have single peaks. II.All symmetric bell-shaped curves are normal. III.All normal curves are bell-shaped and symmetric. A. I only B. II only C. III only D. I and II E. None of the above gives the complete set of true responses. Slide 30 Slide 31 DATA ANALYSIS 66 Below is a scatterplot with one point labeled X. Suppose you find the least squares regression line. Which of the statements on the following slide are true? Slide 32 I.X has the largest residual, in absolute value, of any point on the scatterplot. II.X is an influential point. III.The residual plot will show a curved pattern. A. I only B. II only C. III only D. I and III E. II and III Slide 33 Slide 34 DATA ANALYSIS 67 Data on the number of cancer deaths among Americans (in 1,000s) and years (since 2001) result in the regression line: Deaths= 550 6.05(years) with r = 0.863. What is the correct interpretation of the slope? A. The number of cancer deaths among Americans has been dropping by an average of 6,050 per year since 2001. B. The baseline number of cancer deaths among Americans is 550,000. C. The regression line explains 74.5% of the variation in cancer deaths among Americans over the years since 2001. D. The regression line explains 86.3% of the variation in cancer deaths among Americans over the years since 2001. E. Cancer will be cured in the year 2092. Slide 35