CHAPTER EIGHT
INTERVAL ESTIMATION
MULTIPLE CHOICE-QUESTIONS
In the following multiple-choice questions, circle the correct answer.
1. As the degrees of freedom increase, the t distribution approaches the
a. uniform distribution
b. normal distribution
c. exponential distribution
d. p distribution
2. If the margin of error in an interval estimate of
is 4.6, the interval estimate equals
a.
2.3x
b.
4.6x
c.
4.508x
d.
6.9x
3. The t distribution is a family of similar probability distributions, with each individual
distribution depending on a parameter known as the
a. finite correction factor
b. sample size
c. degrees of freedom
d. standard deviation
4. The probability that the interval estimation procedure will generate an interval that does
not contain the actual value of the population parameter being estimated is the
a. level of significance
b. confidence level
c. confidence coefficient
d. error factor
5. To compute the minimum sample size for an interval estimate of
, we must first
determine all of the following except
a. desired margin of error
b. confidence level
c. population standard deviation
d. degrees of freedom
6. The use of the normal probability distribution as an approximation of the sampling
distribution of
p
is based on the condition that both np and n(1 – p) equal or exceed
a. .05
b. 5
c. 10
d. 30
7. The sample size that guarantees all estimates of proportions will meet the margin of error
requirements is computed using a planning value of p equal to
a. .01
b. .50
c. .51
d. .99
8. We can reduce the margin of error in an interval estimate of p by doing any of the
following except
a. increasing the sample size
b. increasing the planning value p* to .5
c. increasing the level of significance
d. reducing the confidence coefficient
9. In determining an interval estimate of a population mean when
is unknown, we use a t
distribution with
a.
1n−
degrees of freedom
b.
n
degrees of freedom
c. n − 1 degrees of freedom
d. n degrees of freedom
10. The expression used to compute an interval estimate of
may depend on any of the
following factors except
a. the sample size
b. whether the population standard deviation is known
c. whether the population has an approximately normal distribution
d. whether there is sampling error
11. The mean of the t distribution is
a. 0
b. .5
c. 1
d. problem specific
12. An interval estimate is used to estimate
a. the shape of the population’s distribution
b. the sampling distribution
c. a sample statistic
d. a population parameter
13. An estimate of a population parameter that provides an interval believed to contain the
value of the parameter is known as the
a. confidence level
b. interval estimate
c. parameter value
d. population estimate
14. As the sample size increases, the margin of error
a. increases
b. decreases
c. stays the same
d. None of the other answers are correct.
15. The confidence associated with an interval estimate is called the
a. level of significance
b. degree of association
c. confidence level
d. precision
16. The ability of an interval estimate to contain the value of the population parameter is
described by the
a. confidence level
b. degrees of freedom
c. precise value of the population mean
d. None of the other answers are correct.
17. If an interval estimate is said to be constructed at the 90% confidence level, the
confidence coefficient would be
a. 0.1
b. 0.95
c. 0.9
d. 0.05
18. If we want to provide a 95% confidence interval for the mean of a population, the
confidence coefficient is
a. 0.485
b. 1.96
c. 0.95
d. 1.645
19. For the interval estimation of when is assumed known, the proper distribution to use
is the
a. standard normal distribution
b. t distribution with n degrees of freedom
c. t distribution with n – 1 degrees of freedom
d. t distribution with n – 2 degrees of freedom
20. The z value for a 97.8% confidence interval estimation is
a. 2.02
b. 1.96
c. 2.00
d. 2.29
21. It is known that the variance of a population equals 1,936. A random sample of 121 has
been taken from the population. There is a .95 probability that the sample mean will
provide a margin of error of
a. 7.84 or less
b. 31.36 or less
c. 344.96 or less
d. 1,936 or less
22. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of
22. The population standard deviation is known to equal 4.8. The 95.44% confidence
interval for the population mean is
a. 15.2 to 24.8
b. 19.2 to 20.8
c. 19.216 to 20.784
d. 21.2 to 22.8
Exhibit 8-1
In order to estimate the average time spent on the computer terminals per student at a local
university, data were collected from a sample of 81 business students over a one-week period.
Assume the population standard deviation is 1.2 hours.
23. Refer to Exhibit 8-1. The standard error of the mean is
a. 7.5
b. 0.014
c. 0.160
d. 0.133
24. Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately
a. 0.26
b. 1.96
c. 0.21
d. 1.64
25. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is
approximately
a. 7.04 to 110.96 hours
b. 7.36 to 10.64 hours
c. 7.80 to 10.20 hours
d. 8.74 to 9.26 hours
Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length
of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard
deviation of the checkout time is one minute.
26. Refer to Exhibit 8-2. The standard error of the mean equals
a. 0.001
b. 0.010
c. 0.100
d. 1.000
27. Refer to Exhibit 8-2. With a .95 probability, the sample mean will provide a margin of
error of
a. 0.95
b. 0.10
c. .196
d. 1.96
28. Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.80, the standard error
of the mean
a. will increase
b. will decrease
c. remains unchanged
d. becomes negative
29. Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time of all
customers is
a. 3 to 5
b. 1.36 to 4.64
c. 2.804 to 3.196
d. 1.04 to 4.96
Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average
speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally
distributed, with a standard deviation of 13.5 mph.
30. Refer to Exhibit 8-3. If we are interested in determining an interval estimate for
at
86.9% confidence, the z value to use is
a. 1.96
b. 1.31
c. 1.51
d. 2.00
31. Refer to Exhibit 8-3. The value to use for the standard error of the mean is
a. 13.5
b. 9
c. 2.26
d. 1.5
32. Refer to Exhibit 8-3. The 86.9% confidence interval for
is
a. 46.500 to 73.500
b. 57.735 to 62.265
c. 59.131 to 60.869
d. 50 to 70
33. Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the
interval for
would
a. not change
b. become narrower
c. become wider
d. become zero
34. In general, higher confidence levels provide
a. wider confidence intervals
b. narrower confidence intervals
c. a smaller standard error
d. unbiased estimates
35. When the level of confidence increases, the confidence interval
a. stays the same
b. becomes wider
c. becomes narrower
d. cannot tell from the information given
36. A 95% confidence interval for a population mean is determined to be 100 to 120. If the
confidence coefficient is reduced to 0.90, the interval for
a. becomes narrower
b. becomes wider
c. does not change
d. becomes 0.1
37. If we change a 95% confidence interval estimate to a 99% confidence interval estimate,
we can expect the
a. width of the confidence interval to increase
b. width of the confidence interval to decrease
c. width of the confidence interval to remain the same
d. sample size to increase
38. In developing an interval estimate of the population mean, if the population standard
deviation is unknown
a. it is impossible to develop an interval estimate
b. a sample proportion can be used
c. the sample standard deviation and t distribution can be used
d. None of the other answers are correct.
39. A bank manager wishes to estimate the average waiting time for customers in line for
tellers. A random sample of 50 times is measured and the average waiting time is 5.7
minutes. The population standard deviation of waiting time is 2 minutes. Which Excel
function would be used to construct a confidence interval estimate?
a. CONFIDENCE
b. NORMINV
c. TINV
d. INT
40. An auto manufacturer wants to estimate the annual income of owners of a particular
model of automobile. A random sample of 200 current owners is taken. The population
standard deviation is known. Which Excel function would not be appropriate to use to
construct a confidence interval estimate?
a. NORMSINV
b. COUNTIF
c. AVERAGE
d. STDEV
41. Whenever the population standard deviation is unknown, which distribution is used in
developing an interval estimate for a population mean?
a. standard distribution
b. z distribution
c. binomial distribution
d. t distribution
42. The t distribution should be used whenever
a. the sample size is less than 30
b. the sample standard deviation is used to estimate the population standard
deviation
c. the population is not normally distributed
d. None of the other answers are correct.
43. Whenever using the t distribution in interval estimation, we must assume that the
a. sample size is less than 30
b. degrees of freedom equals n − 1
c. population is approximately normal
d. finite population correction factor is necessary
44. From a population that is normally distributed with an unknown standard deviation, a
sample of 25 elements is selected. For the interval estimation of
, the proper
distribution to use is the
a. standard normal distribution
b. z distribution
c. t distribution with 26 degrees of freedom
d. t distribution with 24 degrees of freedom
45. From a population that is not normally distributed and whose standard deviation is not
known, a sample of 50 items is selected to develop an interval estimate for
. Which of
the following statements is true?
a. The standard normal distribution can be used.
b. The t distribution with 50 degrees of freedom must be used.
c. The t distribution with 49 degrees of freedom must be used.
d. The sample size must be increased in order to develop an interval estimate.
46. As the number of degrees of freedom for a t distribution increases, the difference between
the t distribution and the standard normal distribution
a. becomes larger
b. becomes smaller
c. stays the same
d. None of the other answers are correct.
47. The t value with a 95% confidence and 24 degrees of freedom is
a. 1.711
b. 2.064
c. 2.492
d. 2.069
48. A sample of 26 elements from a normally distributed population is selected. The sample
mean is 10 with a standard deviation of 4. The 95% confidence interval for is
a. 6.000 to 14.000
b. 9.846 to 10.154
c. 8.384 to 11.616
d. 8.462 to 11.538
49. A random sample of 36 students at a community college showed an average age of 25
years. Assume the ages of all students at the college are normally distributed with a
standard deviation of 1.8 years. The 98% confidence interval for the average age of all
students at this college is
a. 24.301 to 25.699
b. 24.385 to 25.615
c. 23.200 to 26.800
d. 23.236 to 26.764
50. A random sample of 25 statistics examinations was taken. The average score in the
sample was 76 with a variance of 144. Assuming the scores are normally distributed, the
99% confidence interval for the population average examination score is
a. 70.02 to 81.98
b. 69.82 to 82.18
c. 70.06 to 81.94
d. 69.48 to 82.52
51. A random sample of 25 employees of a local company has been measured. A 95%
confidence interval estimate for the mean systolic blood pressure for all company
employees is 123 to 139. Which of the following statements is valid?
a. 95% of the sample of employees has a systolic blood pressure between 123 and
139.
b. If the sampling procedure were repeated many times, 95% of the resulting
confidence intervals would contain the population mean systolic blood pressure.
c. 95% of the population of employees has a systolic blood pressure between 123
and 139.
d. If the sampling procedure were repeated many times, 95% of the sample means
would be between 123 and 139.
52. To estimate a population mean, the sample size needed to provide a margin of error of 2
or less with a .95 probability when the population standard deviation equals 11 is
a. 10
b. 11
c. 116
d. 117
53. It is known that the population variance equals 484. With a 0.95 probability, the sample
size that needs to be taken to estimate the population mean if the desired margin of error
is 5 or less is
a. 25
b. 74
c. 189
d. 75
54. We can use the normal distribution to make confidence interval estimates for the
population proportion, p, when
a. np 5
b. n(1 – p) 5
c. p has a normal distribution
d. Both np 5 and n(1 – p) 5
EMBS4 TB08 – 10
55. Using an = 0.04, a confidence interval for a population proportion is determined to be
0.65 to 0.75. If the level of significance is decreased, the interval for the population
proportion
a. becomes narrower
b. becomes wider
c. does not change
d. Not enough information is provided to answer this question.
56. In determining the sample size necessary to estimate a population proportion, which of
the following information is not needed?
a. the maximum margin of error that can be tolerated
b. the confidence level required
c. a preliminary estimate of the true population proportion p
d. the mean of the population
57. For which of the following values of p is the value of p(1 – p) maximized?
a. p = 0.99
b. p = 0.90
c. p = 1.0
d. p = 0.50
58. A manufacturer wants to estimate the proportion of defective items that are produced by a
certain machine. A random sample of 50 items is taken. Which Excel function would
not be appropriate to construct a confidence interval estimate?
a. NORMSINV
b. COUNTIF
c. STDEV
d. All are appropriate.
59. A newspaper wants to estimate the proportion of Americans who will vote for Candidate
A. A random sample of 1000 voters is taken. Of the 1000 respondents, 526 say that they
will vote for Candidate A. Which Excel function would be used to construct a
confidence interval estimate?
a. NORMSINV
b. NORMINV
c. TINV
d. INT
PROBLEMS
1. In order to estimate the average electric usage per month, a sample of 196 houses was
selected and the electric usage determined.
a. Assume a population standard deviation of 350 kilowatt hours. Determine the
standard error of the mean.
b. With a 0.95 probability, determine the margin of error.
c. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate
of the population mean?
2. A random sample of 100 credit sales in a department store showed an average sale of
$120.00. From past data, it is known that the standard deviation of the population is
$40.00.
a. Determine the standard error of the mean.
b. With a 0.95 probability, determine the margin of error.
c. What is the 95% confidence interval of the population mean?
3. In order to determine the average weight of carry-on luggage by passengers in airplanes,
a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20
pounds. Assume that we know the standard deviation of the population to be 8 pounds.
a. Determine a 97% confidence interval estimate for the mean weight of the carry–
on luggage.
b. Determine a 95% confidence interval estimate for the mean weight of the carry-
on luggage.
4. A small stock brokerage firm wants to determine the average daily sales (in dollars) of
stocks to their clients. A sample of the sales for 36 days revealed average daily sales of
$200,000. Assume that the standard deviation of the population is known to be $18,000.
a. Provide a 95% confidence interval estimate for the average daily sale.
b. Provide a 97% confidence interval estimate for the average daily sale.
5. A random sample of 121 checking accounts at a bank showed an average daily balance of
$280. The population standard deviation is known to be $60.
a. Is it necessary to know anything about the shape of the distribution of the account
balances in order to make an interval estimate of the mean of all the account
balances? Explain.
b. Find the standard error of the mean.
c. Give a point estimate of the population mean.
d. Construct a 95% confidence interval estimate for the population mean.
e. Interpret the confidence interval estimate that you constructed in part d.
6. A random sample of 49 lunch customers was taken at a restaurant. The average amount
of time the customers in the sample stayed in the restaurant was 33 minutes. From past
experience, it is known that the population standard deviation equals 10 minutes.
a. Compute the standard error of the mean.
b. What can be said about the sampling distribution for the average amount of time
customers spent in the restaurant? Be sure to explain your answer.
c. With a .95 probability, what statement can be made about the size of the margin
of error?
d. Construct a 95% confidence interval for the true average amount of time
customers spent in the restaurant.
e. With a .95 probability, how large of a sample would have to be taken to provide a
margin of error of 2.5 minutes or less?
7. A simple random sample of 144 items resulted in a sample mean of 1080. The
population standard deviation is known to be 240. Develop a 95% confidence interval
for the population mean.
8. A random sample of 26 checking accounts at a bank showed an average daily balance of
$300 and a standard deviation of $45. The balances of all checking accounts at the bank
are normally distributed. Develop a 95% confidence interval estimate for the mean of the
population.
9. A random sample of 81 students at a local university showed that they work an average
of 100 hours per month. The population standard deviation is known to be 27 hours.