Example Multiple Choice Questions

STT 231 - 001 PRACTICE EXERCISES SHEET 1A Example Multiple Choice Questions

1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical

2. The table below summarizes observed data on the gender and party membership of 1000 individuals:

Party Membership Gender Democrat Republican Total Male 300 300 600 Female 200 200 400 Total 500 500 1000

Which one of the following statements about the relationship between gender and party is suggested by the data in the table? A. There is a relationship between gender and party membership. B. There is no relationship between gender and party membership. C. There is a relationship between gender and being a Democrat but not between gender and being a Republican. D. There is a relationship between gender and party membership for males but not for females.

3. Which one of these variables is a categorical variable? A. Number of ear pierces a person has B. Height of a person C. Weight of a person D. Opinion about legalization of marijuana

4. Which one of the following variables is not categorical? A. Age of a person. B. Gender of a person: male or female. C. Choice on a test item: true or false. D. Marital status of a person (single, married, divorced, other)

5. Which of the following is not a term used for a quantitative variable? A. Measurement variable B. Numerical variable C. Continuous variable D. Categorical variable

6. Listed below is the number of Congressional Medals of Honor awarded in wars fought by the United States.

World World War Civil War I War II Korean Vietnam Other Total Medals 1,520 124 440 141 239 105 2,569

What percent of all medals given were awarded during World War I and World War II? A. 4.83% B. 17.13% C. 21.95% D. 78.01%

1 Questions 7 to 9: In a survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of financial assistance. The correspondents were classified as to whether they currently had a child in college or not (college status), and whether they thought the loan obligation for most college students was too high, about right, or too little (loan obligation opinion). The table below summarizes some of the survey results. Use these results to answer the following questions.

Loan Obligation Opinion College Status Too High About Right Too Little Total Child in College 350 80 10 440 No Child in College 250 200 110 560

7. Which type of variable is Loan Obligation Opinion? A. Categorical B. Quantitative C. Continuous D. Measurement

8. What role does the variable Loan Obligation Opinion play in this study? A. Explanatory B. Response C. Confounding D. It plays no role in the study.

9. Which group had the greatest percentage of adults who thought loan obligations are too high? A. Those adults that have a child in college B. Those adults that do not have a child in college C. Both groups have the same percent thinking loan obligations are too high

10. The EPA sends out a survey to learn about people’s water usage habits. Some of the questions included in the survey are given below. Q1. How many times a week do you take a shower? Q2. Do you leave the water running when you brush your teeth? Q3. When you water your lawn, how long do you let the water run?

For each question, determine if it leads to categorical responses or quantitative responses. KEY: Q1 and Q3 lead to quantitative responses, while Q2 leads to categorical responses.

Questions 11 and 12: A USA TODAY/CNN/Gallup Poll conducted April 19, 2005, was based on telephone interviews with 616 U.S. Catholics. One question asked was “When you think about your commitment to the Catholic Church, how much is your commitment affected by who the pope is -- a great deal, a moderate amount, not much, or not at all? The percentages are provided in the table below.

Great deal Moderate Amount Not Much Not at all No Opinion 2005 APR 19 10% 32% 37% 20% 1%

11. The response variable being measured for this question could be called the Commitment Status. State what type of variable commitment status is and suggest an appropriate graph that could be made to display the distribution of this variable. KEY: Commitment status is a categorical variable and an appropriate graph would be a pie chart or bar chart.

12. Approximately how many respondents stated that their commitment is not affected much? KEY: 37% of 616 is 227.92 so approximately 228 respondents answered not much.

13. The percent of data which lie between the lower and upper quartiles is A. 10%. B. 25%. C. 50%. D. 75%. 2 14. A five-number summary for a data set is 35, 50, 60, 70, 90. About what percent of the observations are between 35 and 90? a. 25% b. 50% c. 95% d. 100%

Questions 15 and 16: In a survey, students are asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 9, 14, 20, 60.

15. Which interval describes the number of hours spent studying in a typical week for about 50% of the students sampled? a. 2 to 9 b. 9 to 14 c. 9 to 20 d. 14 to 20

16. Fill in the blank in the following sentence. About 75% of the students spent at least ____ hours studying in a typical week. a. 9 b. 14 c. 20 d. 45

Questions 17 and 18: The following histogram is for the weights (lbs) of 119 female college students. (Source: idealwtwomen dataset on the CD.)

17. What is the approximate shape of the distribution? a. Nearly symmetric. b. Skewed to the left. c. Skewed to the right. d. Bimodal (has more than one peak).

18. The best choice for the median weight for the 119 women based on the histogram is approximately a. 100 pounds. b. 110 pounds. c. 135 pounds. d. 160 pounds.

3 Questions 19 to 21: The following histogram shows the distribution of the difference between the actual and “ideal” weights for 119 female college students. Ideal weights are responses to the question “What is your ideal weight”? The difference = actual ideal. (Source: idealwtwomen dataset on the CD.)

20. The median of the distribution is approximately a. 10 pounds. b. 10 pounds. c. 30 pounds. d. 50 pounds.

21. Most of the women in this sample felt that their actual weight was a. about the same as their ideal weight. b. less than their ideal weight. c. greater than their ideal weight. d. no more than 2 pounds different from their ideal weight.

4 Questions 22 and 23: The following histogram is for the weights (lbs) of 63 male college students. (Source: idealwtmen dataset on the CD.)

22. What is the best description for the approximate shape of this distribution? a. Nearly symmetric. b. Skewed to the left. c. Skewed to the right. d. Bimodal (has more than one peak).

23. The median weight for the 63 men is approximately a. 130 pounds. b. 150 pounds. c. 180 pounds. d. 220 pounds.

5 Questions 24 to 26: The following histogram gives the distribution of the difference between the actual and ideal weights for a sample of male college students. Ideal weights are responses to the question “What is your ideal weight”? The difference = actual ideal.

25. The median of the distribution is approximately a. 10 pounds. b. 0 pounds. c. 10 pounds. d. 20 pounds.

26. Most of the men in this sample felt that their actual weight was a. about the same as their ideal weight. b. less than their ideal weight. c. greater than their ideal weight. d. no more than 2 pounds different from their ideal weight.

6 27. The following boxplot is for the results of the women’s 400-meter dash final race during the 2000 Olympics in Sydney, Australia. Cathy Freeman won in 49.11 seconds. Choose the correct statement about the boxplot.

A. The median time is more than 50 seconds. B. The median time is less than 49.75 seconds. C. The fastest time of 49.11 seconds is an outlier. D. The slowest time of 51.04 seconds is an outlier.

28. Which of the following provides the most information about the shape of a data set? A. Boxplot B. Pie chart C. Five number summary D. Stem-and-leaf plot

Questions 29 to 31: According to a national sleep foundation survey, around 31 million Americans are sleep deprived. They also say women need more sleep than men and are being short-changed. Below are the five number summaries for the number of hours of sleep at night based on a survey of American men and women.

Men: 5.5, 6, 6.5, 7.5, 9 Women: 4.5, 5, 6, 7, 8

29. Write a sentence to compare men versus women in terms of the median amount of sleep at night KEY: The survey shows that the median about of sleep at night for women is 6 hours, about a half an hour less than that for men (which was 6.5 hours).

30. Write a sentence to compare men versus women in terms of the interquartile range for the amount of sleep at night. KEY: Based on the survey, about 50% of the men get between 6 and 7.5 hours of sleep at night, while the interquartile range for women is from 5 to 7 hours of sleep.

31. What percent of women sleep at least 6 hours at night? What percent of men do so? KEY: Based on the survey, about 50% of the women get at least 6 hours of sleep at night, while 75% of men do so.

Questions 32 to 34: A psychologist has developed a new technique intended to improve rote memory. To test the method against other standard methods, 45 high school students are selected at random and each is taught the new technique. The data on the number of words memorized correctly by the students were used to create the following histogram. Note the first class represents the interval [70, 72).

32. What proportion of students memorized correctly at least 94 words? KEY: A total of 8 out of 45 students did so, for a proportion of 0.178 or 17.8%.

33. What is the overall shape of the distribution of the number of memorized words for these students? KEY: The histogram is bimodal, thus showing evidence of two subgroups of students that perhaps should not be aggregated (or combined). The data should be further examined to try to identify the factor that has created these two subgroups.

34. Can we calculate the exact range of the 45 responses? If yes, calculate it. If no, explain why not. KEY: No, we do not know the exact values for the minimum and maximum. We do know that the smallest observation is in the class [70, 72) and thus could be 70 or 71 words. Likewise the largest observation falls in the class [98, 100) and could be 98 or 99 words.

35. Which one of the following statements is most correct about a skewed dataset? A. The mean and median will usually be different. B. The mean and median will usually be the same. C. The mean will always be higher than the median. D. Whether the mean and median are the same depends on whether the data set is skewed to the right or to the left.

Questions 36 to 38: Listed below is a stem-and-leaf plot of the times it took 13 students to drink a 12 ounce beverage. Values for stems represent seconds and values for leaves represent tenths of a second. 3| 1234 3| 5 4| 0 5| 6 6| 11379 7| 8| 2

8 36. What was the median time to drink the beverage? a. 3.5 seconds. b. 4.0 seconds. c. 5.6 seconds. d. 6.9 seconds.

37. The lower quartile is a. 3.1 seconds. b. 3.35 seconds. c. 3.4 seconds. d. 3.5 seconds.

38. The upper quartile is a. 6.9 seconds. b. 6.5 seconds. c. 6.1 seconds. d. 5.6 seconds.

39. Which of the following would indicate that a dataset is skewed to the right? a. The interquartile range is larger than the range. b. The range is larger than the interquartile range. c. The mean is much larger than the median. d. The mean is much smaller than the median.

40. If an exam was worth 100 points, and your score was at the 80th percentile, then a. your score was 80 out of 100. b. 80% of the class had scores at or above your score. c. 20% of the class had scores at or above your score. d. 20% of the class had scores at or below your score.

Questions 41 to 43: The table below provides a statistical summary of the number of CDs owned as reported by students in a class survey done at Penn State University.

Variable N Mean Minimum Q1 Median Q3 Maximum CDs 250 85 0 30 50 100 500

41. Approximately what percent of students own somewhere between 30 and 50 CDs? a. 50% b. 25% c. 20% d. 4%

42. What is the interquartile range for these data? a. 500 b. 100 c. 70 d. 30

43. Based on the summary shown, which of the following statements most likely describes the shape of the CDs owned dataset? a. The summary is evidence that the data are symmetric and bell-shaped. b. The summary is evidence that the data are symmetric but not bell-shaped. c. The summary is evidence that the data are skewed to the left. d. The summary is evidence that the data are skewed to the right.

9 Questions 44 to 47: The following boxplot gives the distribution of the ratings of a new brand of peanut butter for 50 randomly selected consumers (100 points possible with higher points corresponding to a more favorable rating).

44. Based on the boxplot, a. the distribution appears to be skewed to the left. b. the distribution appears to be skewed to the right. c. there appear to be outliers at about 60 and 90. d. there do not appear to be any outliers.

45. The lower quartile is between a. 50 to 60 points. b. 60 to 70 points. c. 70 to 75 points. d. 80 to 90 points.

46. The median is a. 60 points. b. 70 points. c. 75 points. d. 80 points.

47. The upper quartile is between a. 50 to 60 points. b. 60 to 70 points. c. 70 to 75 points. d. 80 to 90 points.

10 48. A recent study was conducted to compare the age of vehicles in a student parking lot versus those in a faculty parking lot at a major university. A random sample of 15 cars was taken from each lot and the age of the car was recorded by taking the current year and subtracting the model year from it. The two boxplots are shown below to summarize these results.

Compare the two distributions based on these side-by-side boxplots. KEY: Overall the faculty cars are newer with a median age of 3 years compared to a median age of 6 years for students’ cars. There was (at least) one faculty car that was much older than the rest and thus shown as an outlier at 7 years. The overall range for the ages of the students’ cars is larger (10 – 1 = 9 years) as compared to the range for the ages of the cars owned by faculty (7 – 0 = 7 years).

11 49. An outlier is a data value that a. is larger than 1 million. b. equals the minimum value in a set of data. c. equals the maximum value in a set of data. d. is not consistent with the bulk of the data.

50. Which statistic is not resistant to an outlier in the data? a. Lower quartile b. Upper quartile c. Median d. Mean

51. Which one of these statistics is unaffected by outliers? a. Interquartile range b. Mean c. Standard deviation d. Range

52. Which one of the following statistics would be affected by an outlier? a. Median b. Standard deviation c. Lower quartile d. Upper quartile

53. Which of the following could account for an outlier in a dataset? a. Natural variability in the measurement of interest. b. Recording the wrong category for an individual's value of a categorical variable. c. A symmetric distribution for the measurement of interest. d. Measuring more than one variable for each individual.

54. By inspection, determine which of the following sets of numbers has the smallest standard deviation. A. 2, 3, 4, 5 B. 4, 4, 4, 5 C. 0, 0, 5, 5 D. 5, 5, 5, 5

Question 55 – 59: Here is a stem-leaf plot of the exam scores of 30 students. 3 | 9 4 | 599 5 | 378 6 | 3677789 7 | 002333556689 8 | 5678 55. The median of this distribution of exam scores is (a) 69 (b) 70 (c) 71 (d) 72 (e) 73

56. The first quartile of this distribution of exam scores is (a) 57 (b) 63 (c) 67 (d) 69 (e) 70

57. If the score 88 is changed to a score 99, the median remains unchanged. (a) true (b) false

58. If the score 88 is changed to a score 99, the mean remains unchanged. (a) true (b) false

12 59. The distribution of scores is best described as (a) symmetrical (b) skewed to the right (c) skewed to the left

Questions 60 – 64. A sample of 1,000 students was cross-tabulated by sex and score on an SAT Exam. The contingency table is shown below. SAT Score Sex 1000 to 1100 to 1300 to 1500 to Total <1100 <1300 <1500 <1600 Female 60 180 240 120 600 Male 60 150 140 50 400 Total 120 330 380 170 1000

60. For the sample of 1,000 students, males make-up what percentage? (a) 10% (b) 20% (c) 30% (d) 40% (e) 50%

61. What percentage of males scored 1300 or above? (a) 50.0% (b) 47.5% (c) 19.0% (d) 14.0% (e) not possible to determine

62. What is the risk of scoring below 1100 for females? (a) 0.1 (b) 0.2 (c) 0.6 (d) 0.01 (e) 0.9

63. What is the relative risk of scoring below 1100 for females relative to males? (a) 0.15 (b) 0.2 (c) 0.85 (d) 0.67 (e) 1

64. When comparing the performance of males and females on the SAT Exam using this sample, which is more appropriate to use? (a) frequencies (b) percents

65. Consider this sample of n=3 scores: 1, 12, 14. The mean and standard deviation of this sample are (a) 9, 8.9 (b) 12, 7 (c) 12, 9 (d) 9, 4.1 (e) none of these

66. Here is a dotplot of n=19 length measurements in cm. The median length is closest to (a) 78 cm (b) 76 cm (c) 81 cm (d) 83 cm (e) 70 cm

. .: ... . . : .: . . ... ------+------+------+------+------+------length 72.0 75.0 78.0 81.0 84.0 87.0

Questions 67 – 73: Below is a boxplot of the examination scores of a large class of students.

15 25 35 45 55 65 75 85 score 13 67. Approximately, what percentage of students scored above 47? (a) 75% (b) 50% (c) 45% (d) 25% (e) 10%

68. The median score is about (a) 34 (b) 43 (c) 30 (d) 39 (e) 41

69. The lowest score is about (a) 17 (b) 34 (c) 39 (d) 48 (e) not possible to determine

70. The highest score is about (a) 17 (b) 57 (c) 75 (d) 85 (e) not possible to determine

71. Approximately, what percentage of students scored between 34 and 39? (a) 50% (b) 40% (c) 35% (d) 25% (e) 75%

72. The third quartile of this distribution is about (a) 17 (b) 34 (c) 39 (d) 47 (e) 75

73. The inter-quartile range (IQR) is about (a) 13 (b) 5 (c) 3 (d) 25% (e) 75%

QUESTIONS 74 – 78

Here is a steam and leaf display of the pulse rate (beats per minute) of 25 women, taken by a researcher at a health clinic.

56 60 4 4 66 7 8 71 2 3 3 76 7 7 7 8 8 80 1 1 2 4 4 4 88

74. The distribution of sample weights is best described as

A. Symmetric about its mean B. Skewed toward large values C. Skewed toward small values D. Multimodal

75. The sample median is A. 76 B. 74 C. 77 D. 80 E. None of these

76. The Inter-quartile range, IQR is A. 20 B. 21 C. 12 D. 13 E. None of these

14 77. Which of the following statement is true?

A. The mean is greater than the median B. The median is greater than the mean C. The mean is equal to the median D. The mean is equal to the mode

78. For this sample, the percentage of women with pulse rate more than 70 is closest to

A. 60.6% B. 60.2% C. 73.9% D. 69.6% E. 72.0%

QUESTIONS 79 – 80 A classroom is furnished with a collection of 32 old chairs, as described in this table:

No Arms Arms Writing Desk Wood 8 5 3 Plastic 5 7 4

79. Approximately what fraction of all chairs have a writing desk attached?

A. 0.094 B. 0.125 C. 0.22 D. 0.25 E. 0.75

80. What fraction of plastic chairs have a writing desk attached?

A. 0.094 B. 0.125 C. 0.22 D. 0.25 E. 0.75

QUESTIONS 81 - 83

Below is a boxplot of the seal strengths of n = 100 sample potato chip bags.

0 10 20 30 40 50 60 70 80 90 100 10. The median seal strength is closest to Seal Strength (a) 6 (b) 15 (c) 25 (d) 30 (e) 20 81. Approximately, what percentage of bags had seal strengths above 15?

A. 50% B. 5% C. 10% D. 25% E. 75%

15 82. Assume that Q1 = 3 and Q3 = 15. What is the value of the upper fence? A. 33 B.18 C.15 D.39 E. 92

83. The distribution of scores is best described as

A. Skewed to the right B. Skewed to the left C. Symmetric about its mean D. Symmetric about its median

84. The weekly salaries (in dollars) of sixteen government workers are listed below.

690 564 813 644 728 535 455 611 491 679 685 356 519 787 489 1086

Identify potential outlier(s), if there is(are) any, in the given data. A. 356 and 986 B. 611 C. 356 D. 1086 E. None

85. The National Education Association collects data on the number of years of teaching experience of high – school teachers. A sample taken this year of 19 high – school teachers yielded the following data on number of years of teaching experience.

16 24 1 34 15 7 18 9 20 14 17 19 16 10 21 25 14 39 18

Identify potential outlier(s), if there is (are) any, in the given data.

A. 34 and 39 B. 1 and 39 C. 1 D. 1, 34 and 39 E. None

16 The death for individual states in 2002. The mortality data for one state is given. Centers for Disease Control lists causes of In this state, what percent of deaths were from causes not listed here? A

17 34.8% B

18 59.1% C

19 70.1% D. 29.9%

20 The individual states Centers in 2002. The mortality data for one state is given. for Disease Control lists causes of death for Is it reasonable to conclude that, in this state, cancer or respiratory diseases were the cause of approximately 29% of deaths in 2002? A

21 Yes, because the percentages can always be added in relative frequency tables. B

22 No, because these categories overlap. C

23 No, because the percentages do not add up to 100%. D

24 No, because the percentages in relative frequencies tables can never be added. E

25 Yes, because these categories do not overlap.

Describe the distribution (shape, center, spread, unusual features).

26 88. The County. In addition to describing the distribution, approximate the percentage histogr of farms that are under100 acres. am shows the sizes (in acres) of 169 farms in Lake A)

27 A. The Lake County is symmetric, with farm sizes ranging from 0 to 450 acres. The mode of the distribution distribution is between 100 and 150 acres. It appears that 118 of 169 farms are under100 of the size acres, approximately 70%. of farms in B

28 The County is skewed to the right. Most of the farms are smaller than 150 acres, with some distribution larger ones, from 150 to 300 acres. Five farms were larger than the rest, over 400 acres. of the size The mode of the distribution is between 0 and 50 acres. It appears that 62 of 169 farms of farms in are under100 acres, approximately 37%. Lake C

29 The Lake County is skewed to the right. Most of the farms are smaller than 150 acres, with distributio some larger ones, from 150 to 300 acres. Five farms were larger than the rest, over 400 n of the acres. The mode of the distribution is between 0 and 50 acres. It appears that 118 of size of 169 farms are under100 acres, approximately 70%. farms in D

30 The County is symmetric, with farm sizes ranging from 0 to 450 acres. The mode of the distribution distribution is between 0 and 50 acres. It appears that 118 of 169 farms are under100 of the size acres, approximately 70%. of farms in Lake E

31 The Lake County is skewed to the right. Most of the farms are smaller than 50 acres, with distribution some larger ones, from 150 to 300 acres. Five farms were larger than the rest, over 400 of the size acres. The mode of the distribution is between 0 and 50 acres. It appears that 118 of 169 of farms in farms are under100 acres, approximately 70%.

Find the median of the data. 89.

32 The stem- and- leaf display shows the results of the mathe matic test of 30 student s.

33 A )

40 87.5

41 E) 8 8 A

42 $560

44 $400

46 $500

48 $450

49 E $8 Hu S ft, St, S ic, l k because kbecause y because d e the e the mthe W wmean is wmean is mmean y e smaller e smaller e and the Solve the o d than the dthan the t median problem. u median median r are close t and the t and the d o upper o lower e quartile quartile s t is farther t is c h from the hfarther r e median e from the i than the median b l lower l than the e e quartile. e upper f quartile. t h i s

d i s t r i b u t i o n

s y m m e t r i c

s 50 Here are boxplot s of the points scored during the first 10 games of the basketb all season for both Carolin e and Alexan dra. Summa rize the similari ties and differe nces in their perfor mance so far.

51 Ter A hga ) eme . gCa irol rine lis smu ch hmo are vco ensi ste ant, bec dau ise fher fIQ eR ris eab nout t4 poi ants v, ewh rile aAl gex ean dr sa's cis oov rer e15.

52 The girls have the same median score of about 18 points per game. Their IQR are different, but this does not give a different anymore information on the girls' performance. average score per game, but D)

53 Both girls game. Alexandra is much more consistent, because her IQR is about 15 points, while Caroline's is over 3. have a median score of about 18 points per E)

54 Both girls median score of about 18 points per game. Caroline is much more consistent, because her IQR is about have a 4 points, while Alexandra's is over 15.

Q u e s t i o n s

The histogram shows the sizes (in acres) of 169 farms in Lake County.

56 93. Which summary statistics would you choose to summarize the center in these data?

A. Median B. Mean C. Mode D. Midrange E. Interquartile Range

94. Which summary statistics would you choose to summarize the spread in these data?

A. Median B. Mean C. Mode D. Range E. Interquartile Range F. Standard Deviation

95. Justify your answers to questions 93 and 94. A. The Median and the Standard Deviation respectively, would be used to summarize the center and spread, of the sizes, in acres, of the 169 farms in Lake County because the distribution is right skewed. B. The Mean and the Interquartile Range respectively, would be used to summarize the center and spread, of the sizes, in acres, of the 169 farms in Lake County because the distribution is right skewed. C. The Midrange and the Range respectively, would be used to summarize the center and spread, of the sizes, in acres, of the 169 farms in Lake County because the distribution is right skewed. D. The Median and the Interquartile Range respectively, would be used to summarize the center and spread, of the sizes, in acres, of the 169 farms in Lake County because the distribution is right skewed. E. The Mean and the Interquartile Range respectively, would be used to summarize the center and spread, of sizes, in acres, of the 169 farms in Lake County because the distribution is right skewed. 96. From the histogram, would you expect the mean or the median to be larger? Explain. A. The median is larger than the mean because the distribution of the sizes, in acres, of the 169 farms in Lake County is skewed to the right. B. The mean is larger than the median because the distribution of the sizes, in acres, of the 169 farms in Lake County is skewed to the right. C. The mean and the median are basically equal because of the presence of at least one outlier. D. All of the above

97. Here are the ages for a sample of n = 5 children: 1, 9, 7, 5, 3. The Mean, M, and the Sample Standard Deviation, SSD, and the Median, MD, are given by

A. M = 4.5; SSD = 3.16; MD = 7 B. M = 5; SSD = 10; MD = 5 C. M = 5.5; SSD = 3.16; MD = 7 D. M = 5; SSD = 3.16; MD = 5 E. M = 6; SSD = 3.4; MD = 7 F. None of the above

57 QUESTIONS 98 – 101

Here are summary statistics for the sizes (in acres) of Finger Lakes vineyards:

Count 36 Mean 46.50 acres Standard Deviation 47.76 Median 33.50 Interquartile Range, IQR 36.50 Minimum 6 Lower Quartile, Q1 18.50 Upper Quartile, Q3 55 Maximum 250

98. The distribution of the sizes (in acres) of Finger Lakes vineyards is

A. Symmetric B. Heavily left – skewed C. Bimodal D. Heavily right – skewed

99. The Upper Fence A. 109.75 B. – 36.25 C. 250 D. 6 C. None of the above

100. The Lower Fence A. 109.75 B. - 36.25 C. 250 D. 6 D. None of the above

101. The data value ______is an outlier.

A. 109.75 B. – 36.25 C. 250 D. 6 E. None of the above

QUESTIONS 102 – 106

A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36oF but he inadvertently recorded the Celsius value of 2o. Assuming that he correctly listed all the other temperatures, state how this error will affect these summary statistics. 58 102. The Mean temperature will A. Increase B. Decrease C. Not change

103. The Median temperature will A. Increase B. Decrease C. Not change

104. The range in temperature will A. Increase B. Decrease C. Stay the same

105. The Interquartile Range (IQR) will A. Increase B. Decrease C. Not change

106. The Standard Deviation in temperature will A. Increase B. Decrease C. Stay (roughly) the same

Some companies offer 401(K) retirement plans to employees, permitting them to shift part of their before-tax salaries into investments such as mutual funds. Employers typically match 50% of the employees’ contribution up to about 6% of salary. One company, concerned with what it believed was a low employee participation rate in its 401(K) plan, sampled 30 other companies with similar plans and asked for their 401(K) participation rates.

107. Identify the WHO

A. All similar companies offering 401(K) retirement plans B. 401(K) employee participation rates (in percent) C. 30 similar companies offering 401(K) retirement plans D. Retirement plans to employees E. None of the above

108. Identify WHAT was investigated

A. 30 similar companies offering 401(K) retirement plan B. All similar companies offering 401(K) retirement plan C. Retirement plans to employees D. 401(K) employee participation rates (in percent) E. None of the above

59 109. Identify the POPULATION IN INTEREST

A. All similar companies offering 401(K) retirement plan B. Retirement plans to employees C. 30 similar companies offering 401(K) retirement plan D. 401(K) employee participation rates (in percent) E. None of the above

Below is a boxplot of the seal strengths of n = 100 sample potato chip bags.

0 10 20 30 40 50 60 70 80 90 100 14. The lower quartile, Q1, the median, MD, andS thee aupperl St quartile,rength Q3, are respectively?

110. The Lower quartile Q1, the Median MD, the Upper quartile Q3, the Lower Fence LF, the Upper Fence UF, are respectively?

A. 0, 6, 34, - 15, 33 B. 3, 6, 15, - 15, 33 C. 1, 7, 15, 0, 102 D. 0, 15, 94, 12, 18 E. 1, 15, 94, 15, 33

111. The dataset of the seal strength of the sample of n = 100 potato chip bags has ______outliers.

A. 6 B. 5 C. 4 D. 3 E. 2

Here are amounts of money (cents) in coins carried by 10 students in a statistics class:

50 35 0 97 76 0 0 87 23 65

60 112. The mean, M; Median, MD; and Standard deviation, SD, of these data are

A. M = 43.3; MD = 42.5; SD = 35.3 B. M = 42.5; MD = 35; SD = 37.2 C. M = 43.3; MD = 42.5; SD = 37.2 D. M = 42.5; MD = 43.3; SD = 37.2 E. M = 43.3; MD = 38; SD = 37.2

113. The five-number summary of this data is

A. 0, 0, 42.5, 76, 97 B. 0, 0.29, 57.5, 81.5, 97 C. 0, 0.29, 42.5, 75, 97 D. 0, 0, 38, 76, 97 E. None of the above

114. You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to $500,000 in price. The few houses on the water, however, have prices up to $15 million. The distribution of house prices will be

A. Skewed to the left B. Roughly symmetric C. Bimodal D. Multi-modal E. Skewed to the right

115. One measure of the difficulty of a golf course is its length: the total distance (in yards) from tee to hole for all 18 holes. Here are the summary statistics for the lengths of all the golf courses in Vermont:

COUNT 45 MEAN 5892.91 YD STANDARD DEVIATION 386.59 MIN 5185 Q1 5585.75 MEDIAN 5928 Q3 6131 MAX 6796

What summary statistics would you use to describe these data?

A. Median and interquartile range (IQR) because the distribution is multimodal. B. Mean and standard deviation because the distribution is roughly unimodal and symmetric. C. Mean and range because the distribution is roughly unimodal and symmetric. D. Median and range because the distribution is roughly unimodal and symmetric. E. Median and interquartile range (IQR) because the distribution displays hidden outliers.

61 QUESTIONS 116 – 117

The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs.

116. Identify the WHO.

A. State Education Department B. Students C. Records on all students D. Local School Districts E. None of the above

117. Identify how many variables the local school districts kept on each student.

A. 5 B. 6 C. 7 D. 4 E. 3

Consider the following weights (in kg) for a sample of twenty-three guinea pigs: 0.98 1.14 1.11 1.00 1.00 1.02 1.00 0.95 0.98 1.29 1.06 1.04 1.08 1.01 1.02 1.03 1.18 1.24 0.97 0.99 1.06 1.09 1.19

Here is a stem-and-leaf plot of the sample data 0.957889 1.000012234 1.06689 1.113 1.189 1.24 1.29

118. The distribution of sample weights is best described as

A. Symmetric about its mean B. Multimodal C. Skewed toward small values (negative skewedness) D. Skewed toward large values (positive skewedness)

119. The sample median weight is

A. 1.00 kg B. 1.02 kg C. 1.025 kg D. 1.03 kg E. 1.04 kg

120. The 1st quartile (Q1) is

A. 1.11 B. 1.08 C. 1.09 D. 1.00 E. None of these

62 121. For this sample, the percentage of guinea pigs with weights less than 1.10 kg is

A. 73.9% B. 65.2% C. 60.9% D. 88.6% E. 78.2%

A sample of 1,400 children was studied to investigate the relationship of the characteristic carrier of Streptococcus pyogenes (2 levels) and the characteristic size of tonsils (3 class intervals). The frequency data are given in the following table.

Tonsil Size (diameter) 0.4 cm - under 0.6 cm 0.6 cm - under 0.8 cm 0.8 cm - 1.0 cm Total Carrier 20 20 50 90 Noncarrier 500 600 210 1310 Total 520 620 260 1400

122. What percentage of the persons with large tonsils (0.8 cm to 1.0 cm in diameter) are carriers?

A. 40% B. 55.6% C. 28.5% D. 19.2% E. 16%

123. The median tonsil diameter for the 90 carriers of Streptococcus pyogenes is in which interval?

A. 0.4 cm - under 0.6 cm B. 0.6 cm - under 0.8 cm C. 620 D. 0.8cm – 1.0cm

The Cleveland Casting Plant is a large highly automated producer of gray and nodular iron automotive castings for Ford Motor Company. The company is interested in keeping the pouring temperature of the molten iron (in degrees Fahrenheit) close to the specified value of 2550 degrees. Cleveland Casting measured the pouring temperature for 10 randomly selected crankshafts.

124. Identify the WHO.

A. Cleveland Casting Plant B. Ford Motor company C. The pouring temperature of the molten iron D. 10 crankshafts at Cleveland Casting Plant E. None of the above

125. Identify WHAT was investigated.

A. The pouring temperature (in degrees Fahrenheit) of molten iron B. Cleveland Casting Plant C. Automotive castings for Ford Company D. Nodular iron E. None of the above

63 126. Identify the POPULATION OF INTEREST.

A. The pouring temperature (in degrees Fahrenheit) of molten iron B. 10 crankshafts at Cleveland Casting C. All crankshafts at Cleveland Casting D. Cleveland Casting Plant E. Ford Motor Company

Here are the annual numbers of deaths from tornadoes in the United States from 1990 through 2000.

53 39 39 33 69 30 25 67 130 94 40

127. The median death from tornadoes in the United States from 1990 through 2000 is

A. 30 B. 40 C. 27.5 D. 39.5 E. 49.5

128. The Inter-quartile range (IQR), from this data, of deaths from tornadoes in the United States from 1990 through 2000 is

A. 98.5 B. 62.5 C. 32 D. 36 E. 68

The Men’s Combined Skiing event consists of a downhill and a slalom. Here is the total times (adding the two race times) for the 2006 Olympics:

Count 35 Mean 196.079 Standard Deviation 5.80009 Min 189.350 Q1 192.238 Median 193.270 Q3 200.625 Max 211.890

64 # of Skiers

Combined Times (Sec)

129. What is the range of these lengths?

A. 22.54 B. 189.350 C. 211.890 D. 8.387 E. 2.809

130. Between what values do the central 50% of these times lie?

A. Between 193.270 and 196.079 B. Between 192.238 and 200.625 C. Between 189.350 and 211.890 D. Between 200.625 and 211.890 E. None of the above

QUESTION 131

An investigation, compiled information about recent nonmilitary plane crashes (www.planecrashinfo.com). The causes, to the extent that they could be determined, are summarized in the table.

CAUSE PERCENT Pilot Error 40 Other Human Error 5 Weather 6 Mechanical Failure 14 Sabotage 6

65 Is it reasonable to conclude that the weather or mechanical failures caused only 20% of the recent plane crashes and what percent of deaths were from causes not listed here?

A. It is not reasonable to conclude that weather or mechanical failures caused only 20% of the recent plane crashes because these categories overlap. The percent of deaths from causes not listed is 29%. B. It is not reasonable to conclude that weather or mechanical failures caused only 20% of the recent plane crashes because the data is left-skewed. The percent of deaths from causes not listed is 29%. C. It is not reasonable to conclude that weather or mechanical failures caused only 20% of the recent plane crashes because the sum of the percent column is only 71%. The percent of deaths from causes not listed is 29%. D. It is reasonable to conclude that weather or mechanical failures caused only 20% of the recent plane crashes as long as each plane crash had only one cause, as it appears to be the case. The percent of deaths from causes not listed is 29%.