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and Instructions other rules: 1. Both the exam and the bubble sheet will be collected 2. You must print your name and sign the honor pledge on the bubble sheet. You must also bubble in your name and your student identification number. 3. Keep in mind that there are 22 questions, each worth 1 point. Each question has only one correct answer. 4. To fill out the bubble sheet, use only "number 2" pencil. Do not use ink. Do not tear or fold the bubble sheet. A grade of zero will be assigned for the entire exam if the bubble sheet is not filled out according to the above instructions. !" 1. The two histograms below are obtained from the same data but using different bins. (In each bin, the left endpoint is included but the right one is not.) 8 6 Count Count 4 2 0 15 20 25 30 35 40 45 50 55 60 Score 15 30 Score 45 60 Note that the vertical axis in the second histogram is not marked by numbers. However, the height of the highest bar in the second histogram is (1) (2) (3) (4) 18. 20. 15. Cannot be determined from the available information 2. Suppose that the variable Z has a standard normal distribution. The point z with 40% of observations falling above it, is about: (1) (2) (3) (4) 0.14. -0.25. 0.25. 0.65. 3. The following data gives the times (in rounded minutes) for the winner of the Boston marathon in the years 1991 to 2001: Year Time 91 92 144 144 93 145 94 142 95 145 96 147 97 146 98 143 99 143 00 146 01 144 Which of the following can be used to describe the distribution of the winning times? (1) (2) (3) (4) Time plot. Box plot. Pie chart. None of the above. 4. The graph 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 is the boxplot of the following data: (1) (2) (3) (4) 10, 20, 25, 30, 35, 40, 40, 45, 50, 80. 10, 20, 25, 30, 35, 35, 40, 45, 50, 80. 10, 20, 25, 30, 35, 35, 40, 45, 50, 90. 10, 20, 20, 30, 35, 35, 40, 45, 50, 80. Page 2 5. Which of the following is true for the standard deviation s? (1) (2) (3) (4) It can happen that s < 0. s is measured in the same units as data. s is a resistant measure. s is not affected by a change in the measurement unit. 6. The mean temperature at noon in Chapel Hill during the month of April, 2004, was 68o F. Recall that the relationship between degrees Fahrenheit xF and degrees Celsius xC is xC = 5(xF 32)/9. Therefore, the mean temperature in degrees Celsius in Chapel Hill at noon that month was (1) (2) (3) (4) 18. 20. 19. Cannot be determined from the available information. 7. Consider the following bar graph of the distribution of job type in a company of 50 employees: 45 Percent of employees 35 25 15 Management Technical Job Type Clerical The number of technicians in the company is (1) (2) (3) (4) 50. 20. 25. Cannot be determined from the available information. 8. Financial data contain information on monthly percent returns on stocks of 5 US companies for each month in the period from July 1990 to May 1997. Which of the following is correct for this data set? (1) (2) (3) (4) Individuals are 5 companies and variable is month. Individuals are months and variables are returns on 5 stocks. Individuals are 5 companies and variable is monthly percent return. None of the above. Page 3 9. Which of the following is correct regarding bins (intervals) in a histogram? (1) (2) (3) (4) Wider bins are preferred because they contain more data. The number of bins is determined by the data size. Bins may have different widths to adapt to the shape of distribution. None of the above. 10. Below is a stemplot of expenditures (in dollars) of 50 shoppers at a supermarket: 0|399 1|13456778899 2|00123455667888 3|25699 4|1345579 5|0359 6|1 7|0 8|366 9|3 Which of the following describes best the shape of the distribution of the expenditures? The distribution is (1) (2) (3) (4) Symmetric. Right-skewed. Symmetric with the outliers 61, 70, 83, 86, 86, 93. Left-skewed. 11. The set-up here is the same as in question 10 above. The median of the distribution of the expenditures is (1) (2) (3) (4) About 49. Cannot be determined exactly because the data size 50 is even. 27.5. Either 27 or 28. 12. Suppose the distribution of middle-age men is normal with mean = 6ft and standard deviation = 2in. (There are 12in in 1ft.) What is the of proportion men taller than 6ft and 6in? (1) (2) (3) (4) 1%. Can be assumed 0. 0.15%. 0.3%. Page 4 13. For a Stat homework, Ben obtained the following graph for a given data: 50 40 Score 30 20 10 Supposing that Ben did the problem correctly, what exactly was he asked to do? (1) (2) (3) (4) Ben was asked to produce a boxplot of the data. Ben was asked to produce a bar graph of the data. Ben was asked to produce a modified boxplot of the data. It can not be determined from the available information. 14. Consider the following density curve of a distribution: 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x What is the proportion of outcomes between -1.5 and 0.5? (1) (2) (3) (4) 1/4. 3/4. 1/5. 1. Page 5 15. The variance s of the data {1, 2, -3} is closest to (1) (2) (3) (4) 4. 7. 6. 5. 2 16. Consider the density curve 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 A 0 1 B 2 C 3 4 5 6 7 8 with three points A, B and C marked on it. At which of these points do the mean and the median fall? (1) (2) (3) (4) A is mean, B is median. B is median, C is mean. B is mean and median. A is median, B is mean. 17. Which of the following is true for the correlation r? (1) It is a resistant measure. (2) 0 r 1. (3) If r is the correlation between x and y, then -r is the correlation between -x and y. (4) None of the above. 18. Which of the following variables one should expect to have a normal distribution? (1) (2) (3) (4) Gross sale of a US company. Length of a successful human pregnancy. Service lifetime of a bulb. None of the above. Page 6 19. Consider the following normal quantile plot of some data: 10 5 Data 0 -5 -10 -15 -3 -2 -1 0 1 Normal Distribution 2 3 This shows that the distribution of the data is (1) (2) (3) (4) Normal. Left-skewed. Symmetric. None of the above. 20. Consider the following scatterplot 12 10 8 6 4 2 0 0 2 x 4 6 of two variables x and y. This is the scatterplot of the data (xi ,yi) given by (1) (2) (3) (4) (4,2), (10,3), (2,4), (1,5). (2,4), (3,10), (4,2), (5,1). (2,4), (3,10), (4,4), (5,1). (2,4), (3,10), (4,2), (5,5). y Page 7 21. The following scatterplot represents the data of two variables: the life expectancy x and the gross domestic product y per person in a country: 35000 30000 25000 20000 15000 10000 5000 0 0 20 40 60 80 100 LIFE EXPECTANCY The relationship between x and y is: (1) (2) (3) (4) Linear. Positively associated. Weak. None of the above. 22. Normal distributions are important because (1) (2) (3) (4) They are symmetric and bell-shaped. They appear as the result of many chance outcomes. They satisfy the 68-95-99.7 rule. Their proportions can be deduced from the standard normal table. GDP Page 8 Answer keys with explanation: 1. (1) 2. (3) 3. (2). Answer is not (1) because time plot does not describe the distribution of the data. Time plot just plots the data with respect to time. 4. (2) 5. (2) 6. (2) 7. (3) 8. (2). Answer is not (3). This is analogous to the example of the number of Babe Ruth home runs we discussed. In that example, individuals are years and variable is number of home runs, and NOT individual is Babe Ruth and variable is number of home runs. 9. (4). Answer is not (2) because bin width is not determined by the number of observations (data size). Having one data set, you may create a new one by repeating each observation. The number of observations then increases by a factor of 2 but the bin width stays the same. Answer is not (3) either. Bins in a histogram have the same width. 10. (2) 11. (3) 12. (3) 13. (4). Answer is neither (1) nor (3). Suppose for instance that you think (1) is correct, that is, Ben was asked to produce a boxplot. Since the whiskers do not stretch out more than 1.5xIQR from the box, the data set does not contain any suspected outliers. Therefore, Ben could have possibly been asked to produce a modified boxplot. Then one does not know exactly with the information provided. 14. (2) 15. (2) 16. (2). It is a homework problem. 17. (3). 18. (2) 19. (3) 20. (2) 21. (2) 22. (2). Answers (1) and (3) refer to properties (and not importance) of normal distributions. Answer (4) has nothing to do with importance. One can produce analogous tables for other distributions. Page 9

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