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QUESTIONS BANK (STAT 110) Use the following to answer questions (1-9): Suppose that you have the following set of numbers: 8, 2, 5, 3, 6, 7, 4, 5. 1. The value of the mean is …….. (A) 5 (B) 4.25 (C) 4 (D) 6.1

2.

The value of the mode is …….. (A) 2 (B) 5 (C) 4

(D) 3

3.

The value of the first quartile (Q1) is …….. (A) 2.5 (B) 3.5 (C) 2 (D) 3.25

4.

The value of the interquartile range (IQR) is ……... (A) 3.15 (B) 4 (C) 3 (D) 3.5

5.

The value of the variance is …….. (A) 5.5 (B) 5 (C) 4.5 (D) 4

6.

The value of the midrange is …….. (A) 4 (B) 5.5 (C) 5 (D) 4.5

7.

The value of the coefficient of variation is …….. (A) 55.4 % (B) 55 % (C) 40 % (D) 50 %

8.

From the values of the mean, median, and mode, you can conclude that the distribution of these data is …….. (A) positively skewed. (C) negatively skewed. (B) symmetric. (D) left-skewed.

9.

The distribution of these data is called …….. distribution. (A) bimodal (B) trimodal (C) unimodal (D) multimodal

10.

If we have measured the weights of a sample of 50 persons and computed their median, this will be an example of …….. statistics. (A) descriptive (B) inferential (C) predictive (D) population

11. Nationality is an example of what level of measurement? (A) ordinal

(B) nominal

(C) ratio

(D) interval

Use the following frequency distribution to answer questions (12-17).

Class Limits Frequency

40-50 3

50-60 60-70 70-80 80-90 Total 4 6 5 2 20

12. The number of classes is …….. (A) 3

(B) 6

(C) 4

(D) 5

13. What is the width of the class 60 -70? (A) 15

(B) 10

(C) 20

(D) 5 -1-

14. The modal class is …….. (A) 70 - 80

(B) 60 - 70

(C) 50 - 60

(D) 40 - 50

15. The value of the range is …….. (A) 50

(B) 45

(C) 40

(D) 55

16. Using

the class 70 - 80, the lower class limit, and the class …… and ……, respectively. (A) 69.5, 75 (B) 69.75, 70 (C) 80, 70 (D) 70, 75

midpoint are

17. What is the cumulative frequency for the class 70 - 80? (A) 16

(B) 12

(C) 18

(D) 17

18. When

data are categorized as Saudi, Egyptian, Syrian, and Sudanese, the most appropriate measure of central tendency is the ……… (A) mean (B) median (C) midrange (D) mode

The following is a histogram for the statistics scores of a group of 50 students.

Use this histogram to answer questions (19-20). 19. The distribution of statistics scores is …….. (A) positively skewed. (C) negatively skewed. (B) right-skewed. (D) symmetric.

20. What do you expect for the values of the mean, median, and mode? (A) mean = median (B) mean > median

21.

(C) mean < median (D) mean = mode

If a student scored 80 points on a test where the mean was 75 and the student's

z-score was 0.5, then the standard deviation, s, must be ……..

(A) 10

(B) 12

(C) 8

(D) 15 -2-

22.

When the distribution is normal or bell-shaped, if a data value is not within the _ _ range [x – 3s , x + 3s], then this value is called …….. (A) the third quartile (B) an outlier (C) the first quartile (D) the midrange

23.

If a variable assumes the values 2, 3, 5, and 8, then this variable is a …….. variable. (A) continuous (C) discrete (B) continuous and quantitative (D) discrete and qualitative

24.

The most appropriate measure of central tendency for the values 2, 3, 6, and 100 is the …….. (A) mean (B) median (C) mode (D) midrange

25.

If a variable can take any value between 0 and 15, then this variable is called a …….. variable. (A) continuous (C) discrete and quantitative (B) discrete (D) continuous and qualitative

26.

When we want to compare the variability of students' weights and heights, we should use the …….. (A) variance (B) range (C) standard deviation (D) coefficient of variation

27.

What is the statistical term for the mean that is obtained by using the data values of a sample drawn from a specific population. (A) parameter (B) statistic (C) variable (D) quantity

28.

If a researcher would like to determine the effect of height on weight, then height is called a (an) …….. variable. (A) dependent (B) outcome (C) confounding (D) independent

29.

Except for rounding error, relative frequencies should add up to what sum? (A) 0 (B) 1 (C) 50 (D) 100

30.

If the mean of 10 values is 50, then the sum of the values is …….. (A) 400 (B) 600 (C) 450 (D) 500

31. The slope of the regression line y' = 10 - 3x is: (A) 2

(B) 5

(C) -5

(D) -3

32. A researcher wants to determine if there is a linear relationship between the number of hours a person goes without sleep (x) and the number of mistakes he makes on a simple test (y). The following data are recorded. n = 6 , ∑ x = 24 , ∑ y = 36 , ∑ xy = 124 , ∑ x2 = 106 The equation of the regression line is: (A) y' = 2 – 14x (C) y' = 14 – 2x (B) y' = -2 + 14x (D) y' = -14 + 2x -3-

33. Determine the type of relationship shown in the figure below.

(A) there is no relationship

(B) positive

(C) negative

(D) curvelinear

34. The correlation coefficient between the amount of fats ‫ كمية لدةون‬which a person eats and his or her weight may be: (A) close to -1 (B) close to 2

(C) close to 1

(D) 0

35. An emergency service center wishes to see whether a relationship between the outside temperature (x) and the number of emergency calls (y) exists. The data are shown here: n = 5 ∑ x = 9 ∑ y = 17 ∑ xy = 28 ∑ x2 = 23 ∑y2 = 71 Compute the value of the correlation coefficient. (A) -0.274 (B) 0.247 (C) 0.274 (D) -0.275 The equation of the regression line between a person's age in years (x) and the number of hours he exercises per week (y) is given by: y' = 25 – 0.4 x. Use the above equation to answer the questions (36-37). 36. The correct statement that represents the relationship between (x) and (y) is: (A) When the number of hours he exercises increases by 1 hour, his age increases by 0.4 years. (B) When the number of hours he exercises decreases by 1 hour, his age decreases by 25 on average. (C) When a person's age increases by 1 year, the number of hours he exercises decreases by 0.4 on average. (D) When a persons's age Increases by 1 year, the number of hours he exercises increases by 0.4 on average.

37. Predict the number of hours a person exercises per week when his age is 50 years. (A) 4

(B) 5

(C) 3

(D) 1.5 -4-

In the study of the relationship between the number of absences (x) and the final grade (y) of 6 students in the statistics class, the data are shown as follows. ∑ x = 42 , ∑ y = 470 , ∑ xy = 3143 , ∑ x2 = 354 , ∑y2 = 37358 Answer the following two questions (38 -39) 38. The slope of the regression line is ……… (A) 3.45 (B) -2.45 (C) -3.45 (D) 2.45

39. The value of the correlation coefficient is ……. (A) -0.82

(B) 1

(C) 0.92

(D) 0.82

40. If the correlation coefficient (r) equals 0.6, then the relationship can be described as …….. (A) weak and linear. (C) positive, strong and nonlinear.

(B) moderate and nonlinear. (D) positive, moderate and linear.

41. As x increase, y decrease and vice versa. Then, the relationship between the two variables, x and y, can be described as: (A) positive relationship (C) no relationship

(B) negative relationship (D) (A) and (B)

42. What is the range of values for the correlation coefficient? (A) -1 to 2

(B) -1 to 1

(C) -2 to 1

(D) -2 to 2

43. If the value of the correlation coefficient equals 0.9, then the type of the relationship is: (A) strong negative (B) strong positive

(C) weak positive (D) moderate negative

A fair die is rolled once. Answer questions (44-46). 44. What is the probability of getting a 4? (A) 5/6 (B) 2/6 (C) 1/6 (D) 6/6

45. What is the probability of getting an even number? (A) 1/6

(B) 3/6

(C) 4/6

(D) 2/6

46. What is the probability of getting a number greater than 3? (A) 1/2

(B) 1

(C) 2/3

(D) 1/3

47. Two fair dice are rolled. What is the probability of getting a sum of 3? (A) 5/18

(B) 2/9

(C) 5/36

(D) 1/18 -5-

A card is drawn from an ordinary deck. Answer questions (48-50). 48. What is the probability of getting a 5. (A) 5/52 (B) 2/26 (C) 3/26 (D) 5/13

49. What is the probability of getting a 10 or a heart? (A) 3/13

(B) 5/52

(C) 2/13

(D) 4/13

50. What is the probability of getting a picture card? (A) 3/13

(B) 5/26

(C) 1/13

(D) 6/13

51. A box contains 2 black balls and 3 red balls. One ball is randomly selected. Find the probability of obtaining a black ball. (A) 3/5 (B) 2/5 (C) 3/10 (D) 4/5 A survey of a sample of undergraduate students in the faculty of Science in a university revealed the following regarding the gender and majors of the students: Major ‫التخصـص‬ Total Biology Physics Mathematics 22 10 8 40 3 5 2 10 25 15 10 50 A student is randomly selected, use the above table to answer questions (52-55) 52. The probability of selecting a male student is ……… (A) 3/5 (B) 4/5 (C) 1/5 (D) 3/10 Gender ‫الجنس‬ Male Female Total

53. The probability of selecting a biology or physics major is …….. (A) 4/5

(B) 2/5

(C) 5/8

(D) 7/10

54. The probability of selecting a male or a mathematics major is …….. (A) 14/25

(B) 21/25

(C) 3/5

(D) 16/25

55. The probability of selecting a biology major, given that the student selected is a female is …….. (A) 1/2 (B) 3/10

(C) 1/3

(D) 1/4

56. The mean of the number of spots that appear when a die is tossed is …….. (A) 2.5

(B) 3

(C) 4

(D) 3.5

57. Which of the following probability values would complete the following probability distribution?

x 0 1 2 P(x) 1/8 3/8 k (A) 1/8

(B) 3/8

(C) 1/4

(D) 1/2 -6-

3 1/4

Let X denote the number of accidents that occur in a city during a week. The following table lists the probability distribution of X. Number of accidents Probability P(x)

3 0.2

4 0.3

5 0.3

6 0.2

Use the probability distribution given above to answer questions (58-59). 58. The mean of the distribution is …….. (A) 3.5 (B) 4.5 (C) 2.5 (D) 3

59. The variance of the distribution is …….. (A) 1.05

(B) 0.89

(C) 0.85

(D) 1.02

60. A survey found that 2 out of 5 students say that they like statistics course. If 3 students are selected at random, find the probability that exactly one student would have liked the statistics course. (A) 0.525 (B) 0.455 (C) 0.432 (D) 0.345

61. If 20% of T.V.s are defective ‫ معيبة‬, the mean and standard deviation of the number of defective T.V.s for a sample of 100 T.V.s are …….. and …….., respectively. (A) 20 and 4 (B) 25 and 4 (C) 20 and 16 (D) 25 and 16

62. If a player rolls one die and gets 6, he wins $120. The cost to play the game is $15. What is the expected value of his gain? (A) $6 (B) $8 (C) $5 (D) $3

63. If a player draws a card from an ordinary deck and gets 10, he wins $104. If he gets a picture, he looses $26. What is the expected value of his gain? (A) $4 (B) $2 (C) $6 (D) $8

64. How many different 2-digit numbers can be formed from the digits in the number 235? (A) 4 (B) 5

(C) 6

(D) 3

65. How many different tests can be made from a test bank of 5 questions if the test consists of 4 questions? (A) 4 (B) 6 (C) 3

(D) 5

Use the following to answer Questions (66-70): The probability that Student A will pass the statistics exam is 0.8, and the probability that student B will pass the same exam is 0.6. Find the following probabilities:

66. Both students (A and B) will pass the exam. (A) 0.16

(B) 0.72

(C) 0.80

(D) 0.48 -7-

67. Only one of them will pass the exam. (A) 0.35

(B) 0.44

(C) 0.36

(D) 0.40

68. Student A will pass the exam and Student B will fail the exam. (A) 0.27

(B) 0.07

(C) 0.63

(D) 0.32

69. At least one of them will pass the exam. (A) 0.95

(B) 0.85

(C) 0.92

(D) 0.80

70. Both students (A and B) will fail the exam. (A) 0.08

(B) 0.50

(C) 0.52

(D) 0.10

71. If X is a discrete random variable with ∑[x2P(x)] = 30 and E(x) = 5. The variance of the probability distribution of X is …….. (A) 2 (B) 1.5 (C) 3 (D) 5 Two dice, A and B, are rolled. Let X represents the sum of the two numbers of spots that will appear. Answer questions (72-74). 72. What is the probability of X = 5 is? (A) 4/36 (B) 1/12 (C) 3/18 (D) 5/6

73. Find the probability: P(A = 2│X = 3). (A) 3/4

(B) 1/2

(C) 5/18

(D) 1/4

74. Find the probability: P(B = 3). (A) 1/6

(B) 5/6

(C) 7/36

(D) 1/2

75. A coin is rolled three times, the probability of getting two tails is …….. (A) 1/2

(B) 3/4

(C) 5/8

(D) 3/8

76. A die is rolled three times, the probability of getting a 3 twice is …….. (A) 5/72

(B) 1/24

(C) 5/36

(D) 1/18

77. The outcomes of each trial in a binomial experiment …….. (A) must be fixed

(B) are dependent

(C) are unlimited

(D) are independent

78. Which of the following is a binomial experiment? (A) Asking 5 people if they are smokers. (B) Rolling a die to see the number of spots appear on the die. (C) Drawing two balls without replacement from a box contains 2 white balls, 5 red balls, and 3 black balls. (D) Asking 50 people which brand of cigarettes they smoke. -8-

In questions (79-81), find probabilities, for each using the standard normal distribution. 79. P(z < 1.25) (A) 0.8944 (B) 0.9944 (C) 0.5845 (D) 0.8499

80. P(z > 2.43) (A) 0.0065

(B) 0.0075

(C) 0.9935

(D) 0.9925

(B) 0.8625

(C) 0.1359

(D) 0.1375

81. P(1 < z < 2) (A) 0.1425

Find the area under the standard normal curve for questions (82) and (83). 82. To the left of z = 1.96. (A) 0.95 (B) 0.0975 (C) 0.0925 (D) 0.975

83. Between z = 1.5 and z = 2.16. (A) 0.9486

(B) 0.0514

(C) 0.9846

(D) 0.0154

84. The mean of the standard normal distribution is …….. (A) 1

(B) 0

(C) 10

(D) 2

85. Approximately what percentage of normally distributed data values will fall within 1 standard deviation above or below the mean? (A) 95% (B) 68% (C) 99.7% (D) 99%

86. Which is not a property of the standard normal distribution? (A) it's symmetric about the mean. (C) it's unimodal.

(B) it's bell-shaped. (D) it's skewed to the right.

87. The standard deviation of all possible sample means equals ………. (A) The population standard deviation. (B) The population standard deviation divided by the population mean (C) The square root of the population standard deviation. (D) The population standard deviation divided by the square root of the sample size. Let X be a normally distributed random variable with a mean of 60 and a standard deviation of 10. Find the probabilities for questions (88 to 91). 88. P(X < 75) (A) 0.0668 (B) 0.8557 (C) 0.9332 (D) 0.9475

89. P(X > 80) (A) 0.9772

(B) 0.9975

(C) 0.9995 -9-

(D) 0.0228

90. P(65 < X < 80) (A) 0.2857

(B) 0.7143

(C) 0.2975

(D) 0.7025

91. P(X = 60) (A) 0

(B) 0.25

(C) 1

(D) 0.5

The time T1 to travel from A to B through city centre (road R1) is normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. The time T2 to travel from A to B through a new ring road (road R2) is normally distributed with a mean of 15 minutes and a standard deviation of 8 minutes. You have 17 minutes to travel from A to B on an important appointment. Using this information, solve questions (92 to 94).

92. P(T1 > 17) (A) 0.2743

(B) 0.2347

(C) 0.4723

(D) 0.4327

(B) 0.0013

(C) 0.4013

(D) 0.4031

93. P(T2 > 17) (A) 0.0031

94. Your correct decision is ……. (A) R1 is better than R2. (C) R2 is better than R1.

(B) Both R1 and R2 are the same. (D) Insufficient information to make a decision.

95. The total area under the standard normal curve is …….. (A) 0

(B) 1

(C) 0.5

(D) 2

96. Approximately what percentage of normally distributed data values will fall within 2 standard deviation above or below the mean? (A) 95% (B) 68% (C) 99.7% (D) 99%

97. The standard normal distribution is …….. (A) skewed to the right. (C) symmetric.

(B) skewed to the left. (D) asymmetric.

The time (X) needed to complete a final examination in a particular college course is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. Answer questions (98 to 100). 98. What is the probability of completing the exam in less than 70 minutes? (A) 0.1587 (B) 0.9655 (C) 0.8413 (D) 0.0345

99. What is the probability that a student will complete the exam in more than 75 minutes but less than 80 minutes? (A) 0.9965

(B) 0.0404

(C) 0.9956 - 11 -

(D) 0.0044

100. The best point estimate of the population mean is the ……. (A) sample mean. (C) sample mode.

(B) sample median. (D) sample midrange.

A research firm conducted a survey to determine the mean amount smokers spend on cigarettes during a day. A sample of 100 smokers revealed that the sample mean is $5 and sample standard deviation is $ 2. Assume that the sample was drawn from a normal population. Answer questions (101-104). 101. The point estimate of the population mean is …….. (A) 2 (B) 5 (C) 6 (D) 100

102. The lower limit of the 95% confidence interval fo r the population mean is …….. (A) 4.5

(B) 5.5

(C) 4.6

(D) 5.6

103. The upper limit of the 95% confidence interval for the population mean is …….. (A) 5.2

(B) 5.5

(C) 6.2

(D) 5.4

104. The width of the 95% confidence interval for the population mean is …… (A) 0.8

(B) 1

(C) 1.2 (D) 0.6

105. The maximum error of estimate is …….. (A) 0.6

(B) 0.4

(C) 0.5

(D) 0.8