1. The population distribution is the probability distribution of the:
A) whole population of a country C) population means
B) population data D) population probabilities
2. The sampling distribution is the probability distribution of a:
A) sample C) sample without replacement
B) sample with replacement D) sample statistic
3. The probability distribution of a sample statistic is the:
A) frequency distribution of that statistic C) sampling distribution of that statistic
B) binomial distribution of that statistic D) Poisson distribution of that statistic
4. A population contains 8 members. The total number of samples of size 4 that you can
select (without replacement) from this population is:
5. A population contains 14 members. The total number of samples of size 8 that you can
select (without replacement) from this population is:
6. The sampling error is:
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 fewer than 30 members is drawn
D) an error that occurs when a sample of 30 or more members is drawn
7. An error that occurs because of chance is called:
A) nonsampling error B) sampling error C) mean error D) probability
error
Chapter 7
8. An error that occurs because of human mistakes is called:
A) nonsampling error B) sampling error C) mean error D) probability
error
9. The mean age of all students at a university is 24 years. The mean age of a random
sample of 100 students selected from this university is 23.6 years. The difference (23.6 –
24 = -0.4) is the:
A) probability error C) sampling error
B) nonsampling error D) population error
10. The mean weekly earnings of all employees of a company are $822. The mean weekly
earnings of a random sample of 25 employees selected from this company is $837. The
difference ($837 – $822 = $15) is the:
A) probability error C) sampling error
B) nonsampling error D) population error
11. The mean price of all magazines published in the United States is $3.65. The mean price
of a random sample of 16 magazines is $4.30. The sampling error is:
12. The mean age of all cars registered in the United States is 7.50 years. The mean age of a
random sample of 1,000 cars is 6.9. The sampling error is:
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
Chapter 7
15. If
nN
is less than or equal to 0.05, the standard deviation of the sampling distribution of
the sample mean is equal to the population standard deviation:
A) divided by the square of the sample size
B) divided by the sample size
C) divided by the square root of the sample size
D) multiplied by the sample size
16. When the sample size is greater than 1, the standard deviation of the sampling
distribution of the sample means 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) Unable to determine
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
and a standard deviation of
is:
A)
n
B)
2n
C)
n
D)
2
n
19. For a continuous random variable x, the population mean and the population standard
deviation are 82 and 18, respectively. You take a simple random sample of 25 elements
from this population. The mean of the sampling distribution of the sample mean is:
20. For a continuous random variable x, the population mean and the population standard
deviation are 139 and 9, respectively. You take a simple random sample of 36 elements
from this population. The mean of the sampling distribution of the sample mean is:
Chapter 7
21. For a continuous random variable x, the population mean and the population standard
deviation are 69 and 15, respectively. Assuming
, the standard deviation of the
sampling distribution of the sample mean for a sample of 16 elements taken from this
population, rounded to two decimals, is:
22. For a continuous random variable x, the population mean and the population standard
deviation are 95 and 40, respectively. Assuming
, the standard deviation of the
sampling distribution of the sample mean for a sample of 49 elements taken from this
population, rounded to two decimals, is:
23. The daily sales at a convenience store have a mean of $1,297 and a standard deviation of
$134. The mean of the sampling distribution of the mean sales of a sample of 17 days for
this convenience store is:
24. The weights of all babies born at a hospital have a mean of 7.3 pounds and a standard
deviation of 0.65 pounds. The mean of the sampling distribution of the mean weight of a
sample of 41 babies born at this hospital is:
25. The daily sales at a convenience store have a mean of $1280 and a standard deviation of
$172. Assuming
, the standard deviation of the sampling distribution of the
mean sales of a sample of 16 days for this convenience store, rounded to two decimal
places, is:
26. The weights of all babies born at a hospital have a mean of 7.4 pounds and a standard
deviation of 0.66 pounds. Assuming
, the standard deviation of the sampling
distribution of the mean weight of a sample of 32 babies born at this hospital, rounded to
three decimal places, is:
Chapter 7
27. 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
D) normally distributed if n is less than 30
28. 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
29. According to the Central Limit Theorem, the sampling distribution of the sample mean is
approximately normal, irrespective of the shape of the population distribution, if:
A) n is 30 or larger C) np and nq are both greater than 5
B) n is less than 30 D) n is 50 or larger
30. To apply the Central Limit Theorem to the sampling distribution of the sample mean, the
required sample is typically large enough if:
A) n is greater than 50 C) n is less than 30
B) n is 50 or less D) n is 30 or larger
31. 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
Chapter 7
32. A continuous random variable x has a right-skewed distribution with a mean of 45 and a
standard deviation of 6. The sampling distribution of the sample mean for a sample of 25
elements taken from this population is:
A) approximately normal C) skewed to the right
B) normal D) skewed to the left
33. A continuous random variable x has a right-skewed distribution 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 C) skewed to the right
B) not normal D) skewed to the left
34. A continuous random variable x has a left-skewed distribution with a mean of 130 and a
standard deviation of 22. The sampling distribution of the sample mean for a sample of
16 elements taken from this population is:
A) approximately normal C) skewed to the right
B) normal D) skewed to the left
35. A continuous random variable x has a left-skewed distribution with a mean of 155 and a
standard deviation of 28. The sampling distribution of the sample mean for a sample of
75 elements taken from this population is:
A) approximately normal C) skewed to the right
B) not normal D) skewed to the left
36. A population has a mean of 98.2 and a standard deviation of 25.2. Assuming
,
the probability, rounded to four decimal places, that the sample mean of a sample of size
89 elements selected from this population will be between 91 and 97 is:
Chapter 7
37. A population has a mean of 60.5 and a standard deviation of 13.5. Assuming
,
the probability, rounded to four decimal places, that the sample mean of a sample of size
35 elements selected from this populations will be between 62.5 and 67.1 is:
38. A population has a normal distribution with a mean of 51.4 and a standard deviation of
8.4. Assuming
, the probability, rounded to four decimal places, that the sample
mean of a sample of size 18 elements selected from this populations will be more than
51.15 is:
39. A population has a normal distribution with a mean of 79.6 and a standard deviation of
13.3. Assuming
, the probability, rounded to four decimal places, that the
sample mean of a sample of size 18 elements selected from this populations will be less
than 80.1 is:
40. The number of hours spent per week on household chores by all adults has a mean of
28.1 hours and a standard deviation of 6.0 hours. The probability, rounded to four
decimal places, that the mean number of hours spent per week on household chores by a
sample of 53 adults will be more than 26.75 is:
41. The time spent commuting from home to work for all employees of a very large company
has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1
minutes. The probability, rounded to four decimal places, that the mean time spent
commuting from home to work by a sample of 21 employees will be between 43.26 and
49.35 minutes is:
42. If you divide the number of elements in a population with a specific characteristic by the
total number of elements in the population, the dividend is the population:
A) mean B) proportion C) distribution D) sampling distribution
Chapter 7
43. If you divide the number of elements in a sample with a specific characteristic by the
total number of elements in the sample, the dividend is the:
A) sample mean C) sample distribution
B) sample proportion D) sampling distribution
44. The mean of the sampling distribution of the sample proportion is equal to the
population:
A) mean B) mean divided by n C) proportion D) proportion divided by n
45. 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) the square root of
/pq n
D)
/pq n
46. In the case of proportion, the sample size is large if:
A) n is greater than or equal to 30 C) n is less than 30
B) np and nq are both less than 5 D) np and nq are both greater than 5
47. The sampling distribution of the sample proportion is approximately normal if:
A) n is greater than or equal to 30 C) np and nq are both greater than 5
B) np and nq are both greater than 10 D) np and nq are both less than 5
48. A company has 411 employees and 104 of them are college graduates. The proportion of
employees of this company who are college graduates, rounded to three decimal places,
is:
49. A class of 61 students has 15 seniors. The proportion of students in this class who are
seniors, rounded to three decimal places, is:
Chapter 7
50. In a sample of 859 adults, 437 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, rounded to three decimal places, is:
Use the following to answer questions 51-52:
Forty percent of all students at a large university live on campus. Suppose you extract a sample
of 115 students from this university. The sample proportion is the proportion of students in this
sample who live on campus.
51. The mean of the sampling distribution of this sample proportion is:
52. The standard deviation of the sampling distribution of this sample proportion, rounded to
four decimal places, is:
Use the following to answer questions 53-54:
Thirty-five percent of all adults read at least one newspaper daily. Suppose you select a sample
of 486 adults. The sample proportion is the proportion of adults in this sample who read at least
one newspaper daily.
53. The mean of the sampling distribution of this sample proportion is:
54. The standard deviation of the sampling distribution of this sample proportion, rounded to
four decimal places, is:
Chapter 7
55. Suppose the proportion of elements of a population that possess a certain characteristic is
0.62. Assuming
, the probability that the sample proportion for a sample of 120
elements drawn from this population is between .62 and .67, rounded to four decimal
places, is approximately:
56. Suppose the proportion of elements of a population that possess a certain characteristic is
0.34. Assuming
, the probability that the sample proportion for a sample of 472
elements drawn from this population is more than .33, rounded to four decimal places, is
approximately:
Use the following to answer questions 57-58:
Suppose that 6.5% or all persons are allergic to penicillin . A sample of 561 persons is selected.
57. The probability that less than 8% of persons in the sample of will be allergic to penicillin,
rounded to four decimal places, is approximately:
58. The probability that 7.5% to 9% of persons in a the sample will be allergic to penicillin,
rounded to four decimal places, is approximately:
Use the following to answer questions 59-60:
A study shows 18.0% of all adult males did not visit their physicians’ offices last year. A sample
of 623 adult males is selected.
59. The probability that more than 18% of adult males in the sample did not visit their
physicians’ offices last year, rounded to four decimal places, is approximately:
Chapter 7
60. The probability that less than 22.5% of adult males in the sample did not visit their
physicians’ offices last year, rounded to four decimal places, is approximately:
61. The following table shows the population probability distribution of x, the random
variable representing the price per ticket, in dollars, for 20 upcoming concerts at a certain
community’s civic center.
Price per Ticket ($)
P(x)
45
0.20
48
0.20
50
0.15
53
?
55
0.25
How many of the 20 concerts will cost $53 per ticket?
62. A population consists of five elements: 5, 6, 8, 10, and 13. You choose a random
sample of three elements from this population (without replacement). Which of the
following is not a possible value of the sample mean?
A) 6.33 B) 8.00 C) 9.33 D) 10.67
63. You select 15 people at random from a population of 10,000 and ask them how many
movies they have rented in the past month. Their responses are:
4 0 6 0 8 3 7 6 5 0 1 4 2 9 5
You know that the mean number of movies rented in the past month by the population is
5.0. Assuming that you made no non-sampling errors, what is the sampling error for the
mean?
Chapter 7
64. Suppose you are analyzing four different brands of soda. The sodium content, in
milligrams, of one can of each of these brands has a distribution with a mean of 45.2 mg
and a standard deviation of 8.8600 mg. You take a random sample of 2 cans from a large
supply of cans including all four brands of soda. Let
x
be the mean of this sample. What
are the mean and standard deviation of the sampling distribution of
x
?
65. The number of hot dogs sold per game at one concession stand at a baseball park is
normally distributed with
= 23,750 and
= 106. You select 13 games at random,
and the mean number of hot dogs sold,
x
, is denoted. What is the standard deviation of
x
, rounded to three decimal places?
Difficulty level: low Objective: Determine the standard deviation of x-bar.
66. For a sample from a normal distribution with standard deviation
, the standard
deviation of the sampling distribution of the sample mean is
/3. What is the size of the
sample?
67. All 1,035 members at a country club take part in a contest to see who can drive a golf ball
the farthest. Each member takes three swings, and his/her best drive is entered into the
contest. The distances of the drives entered into the contest have a mean of 188.3 yards
and a standard deviation of 16.2 yards. You select a sample of 43 drives, what is the
probability, rounded to four decimal places, that the mean of the sample exceeds 192
yards?
68. There are 2,000 bicycles in a community. The owners of 1,250 of these bicycles also own
locks for the bikes. A sample of 184 bicycles is chosen, and it just so happens that the
proportion of bicycles in the sample that have locks is the same as that for the entire
community. How many of the bicycles in the sample have locks?
Chapter 7
69. You ask 2,500 actors in the Screen Actors Guild (SAG) if they have ever appeared in a
production of Shakespeare’s King Lear. 1,225 of them say “yes”, while the others say
“no”. The value p is the proportion of the actors who have appeared in King Lear. You
next draw a random sample of 11 actors from the SAG. What are the mean and standard
70. A company has 15,000 employees and 10,800 of them have completed a particular
training course. Management decides to choose a random sample from all employees.
What is the minimum number of employees that must be in the sample in order to use the
Central Limit Theorem to approximate the distribution of the proportion in the sample
who have taken the training course?
71. Extensive data suggest that the number of overtime hours paid by a large company per
month can be modeled as distribution with mean 3.5 and standard deviation 1.4.
If P1 is the probability that the mean of a sample of size 55 lies in the interval (2.9, 4.1)
and P2 is the probability that the mean of a sample of size 110 lies in the interval (2.9,
4.1), then
A) P1 = P2 B) P1 > P2 C) P1 < P2 D) P1 = 2P2
Chapter 7
72. Suppose the number of books consulted by a student last weekend has distribution
x
Probability
0
0.20
1
0.60
2
0.20
Let X1 and X2 be independent and each have the same distribution as the population.
Determine the missing elements in the table for the sampling distribution of
12
( )/ 2X X X=+
.
x
Probability
0.0
0.0400
0.5
1.0
1.5
2.0
0.0400
0.0
0.0400
0.5
0.2400
1.0
0.4400
1.5
0.2400
2.0
0.0400
73. A continuous random variable x has a normal distribution with a mean of 51 and a
standard deviation of 26. The sampling distribution of the sample mean for a sample of
16 elements has what mean and standard deviation?
Chapter 7
74. A continuous random variable x has a right-skewed distribution with a mean of 72 and a
standard deviation of 36. The sampling distribution of the sample mean for a sample of
100 elements has what mean and standard deviation?
75. A continuous random variable x has a left-skewed distribution with a mean of 101 and a
standard deviation of 72. The sampling distribution of the sample mean for a sample of
64 elements has what mean and standard deviation?
76. A continuous random variable x has a normal distribution with a mean of 65 and a
standard deviation of 21. In the sampling distribution of the sample mean for a sample of
25 elements, what is the z-score for a sample mean of 68.36?