SAMPLING DISTRIBUTIONS: CHAPTER 7
1. Sampling distribution is the probability distribution of a: a. sample statistic
b. sample with replacement c. sample without replacement d. sample
2. If two random samples of sizes n and 1 n are selected independently from two 2 populations with variances 2
1
σ and 2 2
σ , then the standard error of the sampling distribution of the sample mean difference, X1−X2, equals:
a. 2 1 2 2 2 1 σ )/nn σ − b. 2 1 2 2 2 1 σ )/n n σ + c. 2 2 2 1 2 1 n n σ σ − d. 2 2 2 1 2 1 n n σ σ +
3. Probability distribution of a sample statistic is called the: a. frequency distribution of that statistic
b. binomial distribution of that statistic c. sampling distribution of that statistic d. Poisson distribution of that statistic
4. If two random samples of sizes n and 1 n are selected independently from two 2 populations with means µ and 1 µ , then the mean of the sampling distribution of 2 the sample mean difference, X1−X2,equals:
a. µ1+µ2 b. µ1−µ2 c. µ1/µ2 d. µ1µ2
5. The sampling error is defined as:
a. an error that occurs during collection, recording, and tabulation of data b. the difference between the value of a sample statistic and the value of the
corresponding population parameter
c. an error that occurs when a sample of less than 30 elements is drawn d. an error that occurs when a sample of more than 30 elements is drawn 6. An error that occurs because of chance is called the:
a. nonsampling error b. sampling error c. mean error d. probability error
7. An error that occurs because of human mistakes is called the: a. nonsampling error
b. sampling error c. mean error d. probability error
8. The mean age of all students at ISU is 24 years. The mean age of a random sample of 100 students selected from this university is found to be 24.6 years. The
difference 24.6 – 24 = 0.6 is called the: a. probability error
b. nonsampling error c. sampling error d. population error
9. The mean weekly earnings of all employees of a company are $832. The mean weekly earnings of a random sample of 25 employees selected from this company is found to be $847. The difference 847 – 832 = 15 is called the:
a. probability error b. nonsampling error c. sampling error d. population error
10. The mean price of all magazines published in the United States is $3.64. The mean price of a random sample of 16 magazines is found to be $3.47. The sampling error is:
a. $7.11 b. –$.17 c. $.17 d. $.34
11. The mean age of all cars registered in the United States is 8.5 years. The mean age of a random sample of 1000 cars is found to be 9.2 years. The sampling error is:
a. .7 years b. –.7 years c. 17.7 years d. 6.0 years
12. Suppose that the probability p of a success on any trail of a binomial distribution equals .90. Then for which of the following number of trials, n, would the normal distribution provide a good approximation to the binomial distribution?
b. 35 c. 45 d. 55
13. The mean of the sampling distribution of the sample mean is: a. always equal to the sample mean
b. sometimes equal to the population mean c. always equal to the population mean d. always equal to the sampling procedure
14. The mean of the sampling distribution of the sample mean is the mean of:
a. the means of all possible samples of the same size taken from the population b. the frequency distribution of the population
c. the means of all frequency distributions d. one sample
15. If two random samples of sizes n and 1 n are selected independently from two non-2 normally distributed populations, then the sampling distribution of the sample mean difference, X1−X2, is
a. always non-normal b. always normal
c. approximately normal only if n and 1 n are both larger than 30 2 d. approximately normal regardless of n and 1 n 2
16. When the sample size is greater than 1, the standard deviation of the sampling distribution of the sample mean is always:
a. equal to the standard deviation of the population b. smaller than the standard deviation of the population c. greater than the standard deviation of the population d. none of these
17. As the sample size increases, the standard deviation of the sampling distribution of the sample mean:
a. increases b. decreases
c. remains the same d. none of these
18. The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of µ and a standard deviation of σ is:
a. σ / n b. σ / 2n c. σ/ n d. σ / n2
19. For a random variable x, the population mean and the population standard deviation are 80 and 15 respectively. A sample of 25 elements is taken from this population. The mean of the sampling distribution of the sample mean is:
a. 16 b. 3 c. 80 d. 15
20. For a random variable x, the population mean and the population standard deviation are 54 and 12 respectively. A sample of 36 elements is taken from this population. The mean of the sampling distribution of the sample mean is:
a. 54 b. 12 c. 2 d. 9
21. The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean X :
a. is approximately normal if n > 30 b. is approximately normal if n < 30
c. is approximately normal if the underlying population is normal d. has the same variance as the population
22. For a random variable x, the population mean and the population standard deviation are 100 and 20 respectively. The standard deviation of the sampling distribution of the sample mean for a sample of 16 elements taken from this population is:
a. 20 b. 25 c. 4 d. 5
23. For a random variable x, the population mean and the population standard deviation are 77 and 21 respectively. The standard deviation of the sampling distribution of the sample mean for a sample of 49 elements taken from this population is:
a. 3 b. 11 c. 21 d. 7
24. The expected value of the sampling distribution of the sample mean X equals the population mean µ:
a. when the population is normally distributed b. when the population is symmetric
c. when the population size N > 30 d. for all populations
25. The daily sales at a convenience store have a mean of $1350 and a standard deviation of $150. The mean of the sampling distribution of the mean sales of a sample of 25 days for this convenience store is:
a. $1350 b. $270 c. $30 d. $6750
26. The weights of all babies born at a hospital have a mean of 8.4 pounds and a standard deviation of .70 pounds. The mean of the sampling distribution of the mean weight of a sample of 49 babies born at this hospital is:
a. 1.2 pounds b. 8.4 pounds c. .10 pounds d. 7.0 pounds
27. If all possible samples of size n are drawn from an infinite population with a mean of µ and a standard deviation of σ, then the standard error of the sample mean is inversely proportional to:
a. µ b. σ c. p d. √n
28. The daily sales at a convenience store have a mean of $1350 and a standard deviation of $150. The standard deviation (or standard error) of the sampling distribution of the mean sales of a sample of 25 days for this convenience store is:
a. $150 b. $30 c. $270 d. $750
29. The weights of all babies born at a hospital have a mean of 8.4 pounds and a standard deviation of .70 pounds. The standard deviation of the sampling
distribution of the mean weight of a sample of 49 babies born at this hospital is: a. .10 pounds
b. .70 pounds c. 1.2 pounds d. 8.4 pounds
30. If the population from which samples are drawn is normally distributed, then the sampling distribution of the sample mean is:
a. not normally distributed
b. normally distributed if n is 30 or larger c. always normally distributed
31. The standard deviation of the sampling distribution of the sample mean is also called the:
a. central limit theorem b. standard error of the mean
c. finite population correction factor d. population standard deviation
32. If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is:
a. never normally distributed
b. approximately normally distributed if n is 30 or larger c. always normally distributed
d. approximately normally distributed if n is less than 30
33. According to the central limit theorem, the sampling distribution of the sample mean is approximately normal, irrespective of the population distribution, if:
a. n is 30 or larger b. n is less than 30
c. np and nq are both greater than 5 d. all of the above
34. If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be:
a. normal for all values on n b. normal only for n > 30
c. approximately normal for all values of n d. approximately normal only for n > 30
35. To apply the central limit theorem to the sampling distribution of the sample mean, the sample is considered to be large if:
a. n is greater than 50 b. n is 50 or larger c. n is larger than 40 d. n is 30 or larger
36. A continuous random variable x has a normal distribution with a mean of 90 and a standard deviation of 15. The sampling distribution of the sample mean for a sample of 16 elements taken from this population is:
a. not normal b. normal
c. skewed to the right d. skewed to the left
37. If all possible samples of size n are drawn from a population, the probability distribution of the sample mean X is called the:
b. expected value of X
c. sampling distribution of X
d. normal distribution
38. A continuous random variable x has a distribution that is skewed to the right (such as negative exponential) with a mean of 45 and a standard deviation of 6. The sampling distribution of the sample mean for a sample of 5 elements taken from this population is:
a. approximately normal b. normal
c. skewed to the right d. skewed to the left
39. A random variable x has a distribution that is skewed to the right with a mean of 80 and a standard deviation of 12. The sampling distribution of the sample mean for a sample of 50 elements taken from this population is:
a. approximately normal b. not normal
c. skewed to the right d. skewed to the left
40. Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals:
a. 12.649 b. 25.0 c. 2.56 d. 3.125
41. A random variable x has a distribution that is skewed to the left with a mean of 130 and a standard deviation of 22. The sampling distribution of the sample mean for a sample of 6 elements taken from this population is:
a. approximately normal b. normal
c. skewed to the right d. skewed to the left
42. A population has a mean of 100 and a standard deviation of 27. The probability that the sample mean of a sample of 81 elements selected from this population will be between 91 and 97 is:
a. .4987 b. .3413 c. .1574 d. .8400
43. Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is
a. .4332 b. .0668 c. .0987 d. .9013
44. A population has a mean of 64 and a standard deviation of 12. The probability that the sample mean for a sample of 36 elements selected from this population will be between 62.5 and 67.1 is:
a. .7128 b. .2734 c. .1660 d. .8134
45. A population has a normal distribution with a mean of 48 and a standard deviation of 9. The probability that the sample mean for a sample of 25 elements selected from this population will be more than 51.15 is:
a. .4599 b. .9599 c. .0401 d. .7814
46. A population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:
a. 2.50 b. 12.50 c. 1.5 d. 1.343
47. A population has a normal distribution with a mean of 85 and a standard deviation of 14. The probability that the sample mean for a sample of 16 elements selected from this population will be less than 80.10 is:
a. .4192 b. .9192 c. .4332 d. .0808
48. The number of hours spent per week on household chores by all adults have a mean of 28 hours and a standard deviation of 7 hours. The probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is:
a. .1056 b. .8944
c. .3944 d. .6056
49. An infinite population has a mean of 60 and a standard deviation of 8. A sample of 50 observations will be taken at random from this population. The probability that the sample mean will be between 57 and 62 is
a. .9576 b. .9960 c. .2467 d. .3520
50. The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 42 minutes and a standard deviation of 12 minutes. The probability that the mean time spent commuting from home to work by a sample of 16 employees of this company will be between 43.26 and 49.35 minutes is:
a. .3301 b. .6557 c. .4929 d. .9929
51. The number of elements in a population with a specific characteristic divided by the total number of elements in the population is called the population:
a. mean b. proportion c. distribution
d. sampling distribution
52. If all possible samples of size n are drawn from an infinite population with a mean of 15 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 only for samples of size
a. 5 b. 15 c. 25 d. 75
53. The number of elements in a sample with a specific characteristic divided by the total number of elements in the sample is called the:
a. sample mean
b. sample proportion ( pˆ ) c. sample distribution d. sampling distribution
54. The mean of the sampling distribution of the sample proportion is equal to the population:
b. mean divided by n c. proportion
d. proportion divided by n
55. If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either
a. .4 or .6 b. .5 or .5 c. .2 or .8 d. .3 or .7
56. The standard deviation of the sampling distribution of the sample proportion is equal to:
a. the population standard deviation divided by the square root of n b. the population standard deviation divided by n
c. pq/n
d. pq / n
57. In the case of proportion, normal distribution can be applied if: a. n is greater than or equal to 30
b. np and nq are both less than 5 c. n is less than 30
d. np and nq are both greater than 5
58. The normal distribution is used to approximate the sampling distribution of the sample proportion only if
a. a. the sample size n is greater than 30
b. b. the population proportion p is close to 0.50 c. c. the underlying population is normal
d. np and nq are both greater than 5
59. The sampling distribution of the sample proportion is approximately normal if: a. n is greater than or equal to 30
b. np and nq are both greater than 10 c. np and nq are both greater than 5 d. np and nq are both less than 5
60. A company has 500 employees and 200 of them are college graduates. The proportion of all employees who are college graduates is:
a. .60 b. .50 c. .20 d. .40
61. Random samples of size 49 are taken from an infinite population whose mean is 300 and standard deviation is 21. The mean and standard error of the sample mean are:
a. 300 and 21 b. 300 and 3 c. 70 and 230 d. 49 and 21
62. In a class of 50 students, 12 are seniors. The proportion of students in this class who are seniors is:
a. .12 b. .24 c. .36 d. .88
63. A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is
a. .0166 b. .0228 c. .3708 d. .0394
64. In a sample of 800 adults, 560 are in favor of banning all advertisements relating to alcohol. The proportion of these adults who are in favor of banning all
advertisements relating to alcohol is: a. .70
b. .56 c. .44 d. .30
65. Forty percent of all students at a large university live on campus. Suppose a sample of 100 students is selected from this university and the sample proportion is defined as the proportion of students in this sample who live on campus. The mean of the sampling distribution of this sample proportion is:
a. .60 b. .40 c. .10 d. 100
66. A sample of size 200 will be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is
a. .281 b. .719 c. .580 d. .762
67. Forty percent of all students at a large university live on campus. Suppose a sample of 100 students is selected from this university and the sample proportion is defined as the proportion of students in this sample who live on campus. The standard deviation of the sampling distribution of this sample proportion is:
a. .049 b. .068 c. .273 d. .105
68. Thirty-five percent of all adults read at least one newspaper daily. Suppose a sample of 500 adults is selected and the sample proportion is defined as the proportion of adults in this sample who read at least one newspaper daily. The mean of the sampling distribution of this sample proportion is:
a. .35 b. .65 c. .175 d. .5
69. A sample of size 40 will be taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean will be larger than 70 is
a. .3970 b. .4332 c. .1469 d. .0668
70. Thirty-five percent of all adults read at least one newspaper daily. Suppose a sample of 500 adults is selected and the sample proportion is defined as the proportion of adults in this sample who read at least one newspaper daily. The standard deviation of the sampling distribution of this sample proportion is:
a. .138 b. .512 c. .021 d. .257
71. Suppose the proportion of elements of a population that possess a certain
characteristic is .60. The probability that the sample proportion for a sample of 100 elements drawn from this population is between .62 and .67 is approximately:
a. .4236 b. .1591 c. .2645 d. .5827
72. A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true?
b. The standard error of the sample mean decreases c. The population standard deviation increases d. The standard error of the sample mean increases
73. Suppose the proportion of elements of a population that possess a certain
characteristic is .30. The probability that the sample proportion for a sample of 500 elements drawn from this population is more than .33 is approximately:
a. .0668 b. .4332 c. .9332 d. .0228
74. Suppose that 10% of all persons are allergic to penicillin. The probability that less than 8% of persons in a sample of 1000 will be allergic to penicillin is
approximately: a. .9868 b. .4868 c. .0237 d. .0132
75. If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population must be either:
a. .25 b. .75 c. .20 or .80 d. .35 or .65 e. .30 or .70
76. Suppose that 10% of all persons are allergic to penicillin. The probability that 7.5% to 9% of persons in a sample of 1000 will be allergic to penicillin is approximately:
a. .8638 b. .1308 c. .4973 d. .3665
77. Twenty percent of all adult males did not visit their physicians' offices last year. The probability that more than 18% of adult males in a sample of 800 did not visit their physicians' offices last year is approximately:
a. .9236 b. .4236 c. .0764 d. .1378
78. Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:
a. 9 and 45 b. 45 and 9 c. 81 and 45 d. 45 and 1
79. Twenty percent of all adult males did not visit their physicians' offices last year. The probability that less than 23% of adult males in a sample of 800 did not visit their physicians' offices last year is approximately:
a. .0162 b. .4838 c. .2389 d. .9838
80. A sample of 250 observations will be selected at random from an infinite
population. Given that the population proportion is .25, the standard error of the sampling distribution of the sample proportion is:
a. .0274 b. .50 c. .00075 d. .0548
81. The number of hot dogs sold per game at one concession stand at a baseball park is normally distributed with µ = 23,400 and σ = 105. Ten games are selected at random, and the mean number of hot dogs sold is denoted x . What is the standard deviation ofx ?
a. 35.0 b. 33.204 c. 31.659 d. 30.311
82. If two populations are normally distributed, the sampling distribution of the sample mean difference X1 −X2will be:
a. approximately normally distributed
b. normally distributed only if both sample sizes are greater than 30 c. normally distributed
d. normally distributed only if both population sizes are greater than 30 83. For a sample from a normal distribution with σ = 45, the standard deviation of the
sampling distribution of the sample mean is 15. What is the size of the sample? a. 3
b. 6 c. 9 d. 12
84. Two samples are selected at random from two independent normally distributed populations. Sample 1 has 49 observations and has a mean of 10 and a standard deviation of 5. Sample 2 has 36 observations and has a mean of 12 and a standard deviation of 3. The standard error of the sampling distribution of the sample mean difference is a. .1853 b. .7602 c. .7331 d. .8719 ANSWER KEY: 1. a 2. d 3. c 4. b 5. b 6. b 7. a 8. c 9. c 10. b 11. a 12. d 13. c 14. a 15. c 16. b 17. b 18. c 19. c 20. a 21. a 22. d 23. a 24. d 25. a 26. b 27. d 28. b 29. a 30. c 31. b 32. b 33. a 34. a 35. d 36. b 37. c 38. c 39. a 40. d 41. d 42. c 43. b 44. a 45. c 46. c 47. d 48. b 49. a 50. a 51. b 52. c 53. b 54. c 55. d 56. c 57. d 58. d 59. c 60. d 61. b 62. b 63. a 64. a 65. b 66. b 67. a 68. a 69. c 70. c 71. c 72. b 73. a 74. d 75. c 76. b 77. a 78. d 79. d 80. a 81. b 82. c 83. c 84. d
