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Confidence Interval Estimation195
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATION
1. The width of a confidence interval estimate for a proportion will be
a) narrower for 99% confidence than for 95% confidence.
b) wider for a sample size of 100 than for a sample size of 50.
c) narrower for 90% confidence than for 95% confidence.
d) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion, properties, width
2. When determining the sample size for a proportion for a given level of confidence and sampling
error, the closer to 0.50 that p is estimated to be, the __________ the sample size required.
a) smaller
b) larger
c) The sample size is not affected.
d) The effect cannot be determined from the information given.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion, properties
3. A 99% confidence interval estimate can be interpreted to mean that
a) if all possible samples are taken and confidence interval estimates are developed, 99% of
them would include the true population mean somewhere within their interval.
b) we have 99% confidence that we have selected a sample whose interval does include the
population mean.
c) both of the above
d) none of the above
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, interpretation
4. If you were constructing a 99% confidence interval of the population mean based on a sample of n
= 25, where the standard deviation of the sample s = 0.05, the critical value of t will be
a) 2.7970.
b) 2.7874.
c) 2.4922.
d) 2.4851.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: critical value, t distribution
5. Which of the following is NOT true about the Student’s t distribution? 196 Confidence Interval Estimation
a) It has more area in the tails and less in the center than does the normal distribution.
b) It is used to construct confidence intervals for the population mean when the population
standard deviation is known.
c) It is bell shaped and symmetrical.
d) As the number of degrees of freedom increases, the t distribution approaches the normal
distribution.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t distribution, properties
6. True or False: The t distribution is used to construct confidence intervals for the population mean
when the population standard deviation is unknown.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, standard deviation unknown
7. The t distribution
a) assumes the population is normally distributed.
b) approaches the normal distribution as the sample size increases.
c) has more area in the tails than does the normal distribution.
d) all of the above
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t distribution, properties
8. It is desired to estimate the average total compensation of CEOs in the Service industry. Data were
randomly collected from 18 CEOs and the 97% confidence interval was calculated to be
($2,181,260, $5,836,180). Which of the following interpretations is correct?
a) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.
b) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260
to $5,836,180.
c) In the population of Service industry CEOs, 97% of them will have total compensations
that fall in the interval $2,181,260 to $5,836,180.
d) We are 97% confident that the average total compensation of all CEOs in the Service
industry falls in the interval $2,181,260 to $5,836,180.
ANSWER:
d
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: confidence interval, interpretation Confidence Interval Estimation197
9. It is desired to estimate the average total compensation of CEOs in the Service industry. Data were
randomly collected from 18 CEOs and the 97% confidence interval was calculated to be
($2,181,260, $5,836,180). Based on the interval above, do you believe the average total
compensation of CEOs in the Service industry is more than $3,000,000?
a) Yes, and I am 97% confident of it.
b) Yes, and I am 78% confident of it.
c) I am 97% confident that the average compensation is $3,000,000.
d) I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level.
ANSWER:
d
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: confidence interval, interpretation
10. A confidence interval was used to estimate the proportion of statistics students that are females. A
random sample of 72 statistics students generated the following 90% confidence interval: (0.438,
0.642). Based on the interval above, is the population proportion of females equal to 0.60?
a) No, and we are 90% sure of it.
b) No. The proportion is 54.17%.
c) Maybe. 0.60 is a believable value of the population proportion based on the information
above.
d) Yes, and we are 90% sure of it.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion, testing
11. A confidence interval was used to estimate the proportion of statistics students that are female. A
random sample of 72 statistics students generated the following 90% confidence interval: (0.438,
0.642). Using the information above, what size sample would be necessary if we wanted to
estimate the true proportion to within ± 0.08 using 95% confidence?
a) 105
b) 150
c) 420
d) 597
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: proportion, sample size determination 198 Confidence Interval Estimation
12. When determining the sample size necessary for estimating the true population mean, which factor
is NOT considered when sampling with replacement?
a) the population size
b) the population standard deviation
c) the level of confidence desired in the estimate
d) the allowable or tolerable sampling error
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mean, sample size determination
μ
13. Suppose a 95% confidence interval for turns out to be (1,000, 2,100). Give a definition of what
it means to be “95% confident” in an inference.
a) In repeated sampling, the population parameter would fall in the given interval 95% of the
time.
b) In repeated sampling, 95% of the intervals constructed would contain the population mean.
c) 95% of the observations in the entire population fall in the given interval.
d) 95% of the observations in the sample fall in the given interval.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, interpretation
14. Suppose a 95% confidence interval for turns out to be (1,000, 2,100). To make more useful
inferences from the data, it is desired to reduce the width of the confidence interval. Which of the
following will result in a reduced interval width?
a) Increase the sample size.
b) Decrease the confidence level.
c) Increase the sample size and decrease the confidence level.
d) Increase the confidence level and decrease the sample size.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, properties, width Confidence Interval Estimation 199
15. Suppose a 95% confidence interval forμ has been constructed. If it is decided to take a larger
sample and to decrease the confidence level of the interval, then the resulting interval width would
. (Assume that the sample statistics gathered would not change very much
for the new sample.)
a) be larger than the current interval width
b) be narrower than the current interval width
c) be the same as the current interval width
d) be unknown until actual sample sizes and reliability levels were determined
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, properties, width
16. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the
sample size will lead to a interval.
a) narrower
b) wider
c) less significant
d) biased
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: confidence interval, properties, width
17. A major department store chain is interested in estimating the average amount its credit card
customers spent on their first visit to the chain’s new store in the mall. Fif2een credit card accounts
were randomly sampled and analyzed with the following resultX = $50.50 and s = 400 .
Assuming the distribution of the amount spent on their first visit is approximately normal, what is
the shape of the sampling distribution of the sample mean that will be used to create the desired
confidence interval for ?
a) approximately normal with a mean of $50.50
b) a standard normal distribution
c) a t distribution with 15 degrees of freedom
d) a t distribution with 14 degrees of freedom
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution 200 Confidence Interval Estimation
18.A major department store chain is interested in estimating the average amount its credit card
customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts
were randomly sampled and analyzed with the following results: and 2 .
X = $50.50 s = 400
Construct a 95% confidence interval for the average amount its credit card customers spent on
their first visit to the chain’s new store in the mall, assuming that the amount spent follows a
normal distribution.
a) $50.50 ± $9.09
b) $50.50 ± $10.12
c) $50.50 ± $11.00
d) $50.50 ± $11.08
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
19. Private colleges and universities rely on money contributed by individuals and corporations for
their operating expenses. Much of this money is put into a fund called an endowment, and the
college spends only the interest earned by the fund. A recent survey of 8 private colleges in the
United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0,
122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean
endowment of all private colleges in the United States?
a) $1,447.8
b) $180.975
c) $143.042
d) $8
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: point estimate, mean
20.Private colleges and universities rely on money contributed by individuals and corporations for
their operating expenses. Much of this money is put into a fund called an endowment, and the
college spends only the interest earned by the fund. A recent survey of 8 private colleges in the
United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0,
122.6, 177.5, 95.4, and 220.0. Summary statistics yield and s =143.042 .
X = 180.975
Calculate a 95% confidence interval for the mean endowment of all the private colleges in the
United States, assuming a normal distribution for the endowments.
a) $180.975 ± $94.066
±
b) $180.975 $99.123
c) $180.975 ± $116.621
d) $180.975 ± $119.605
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution Confidence Interval Estimation 201
21. A university system enrolling hundreds of thousands of students is considering a change in the way
students pay for their education. Presently the students pay $55 per credit hour. The university
system administrators are contemplating charging each student a set fee of $750 per quarter,
regardless of how many credit hours each takes. To see if this proposal would be economically
feasible, the administrators would like to know how many credit hours, on the average, each
student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per
quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted
to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard
deviation provided a good estimate for the population standard deviation. How large a sample
would they need to take?
ANSWER:
n = 2033
TYPE: PR DIFFICULTY: Easy
KEYWORDS: mean, sample size determination
22. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-hour
period. The director randomly selects 64 different 24-hour periods and determines the number of
2
admissions for each. For this sampleX = 19.8 and s = 25. Which of the following assumptions
is necessary in order for a confidence interval to be valid?
a) The population sampled from has an approximate normal distribution.
b) The population sampled from has an approximate t distribution.
c) The mean of the sample equals the mean of the population.
d) None of these assumptions are necessary.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution
23. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-hour
period. The director randomly selects 64 different 24-hour periods and determines the number of
admissions for each. For this sampleX = 19.8 and s = 25. Estimate the mean number of
admissions per 24-hour period with a 95% confidence interval.
ANSWER:
19.8 ± 1.249
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution 202 Confidence Interval Estimation
24. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-hour
period. The director randomly selects 64 different224-hour periods and determines the number of
admissions for each. For this samplX = 19.8 and s = 25. If the director wishes to estimate the
mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what
size sample should she choose?
ANSWER:
n = 166
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: mean, sample size determination
25. A university dean is interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean randomly selects 200
students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to
estimate the true proportion of students who receive financial aid.
ANSWER:
0.59 0.057
±
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion
26. A university dean is interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean randomly selects 200
students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p
is 0.59± 0.07. Interpret this interval.
a) We are 95% confident that the true proportion of all students receiving financial aid is
between 0.52 and 0.66.
b) 95% of the students get between 52% and 66% of their tuition paid for by financial aid.
c) We are 95% confident that between 52% and 66% of the sampled students receive some
sort of financial aid.
d) We are 95% confident that 59% of the students are on some sort of financial aid.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion, interpretation Confidence Interval Estimation203
27. A university dean is interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean randomly selects 200
students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the
proportion of all students receiving financial aid to within 3% with 99% reliability, how many
students would need to be sampled?
a) n = 1,844
b) n = 1,784
c) n = 1,503
d) n = 1,435
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: proportion, sample size determination
28. An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. A random sample of 50 individuals resulted
in an average income of $15,000. What is the upper end point in a 99% confidence interval for the
average income?
a) $15,052
b) $15,141
c) $15,330
d) $15,364
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, standardized normal distribution
29. An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. A random sample of 50 individuals resulted
in an average income of $15,000. What is the width of the 90% confidence interval?
a) $232.60
b) $364.30
c) $465.23
d) $728.60
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: width, confidence interval, mean, standardized normal distribution 204 Confidence Interval Estimation
30. An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. A random sample of 50 individuals resulted
in an average income of $15,000. What sample size would the economist need to use for a 95%
confidence interval if the width of the interval should not be more than $100?
a) n = 1537
b) n = 385
c) n = 40
d) n = 20
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mean, sample size determination
31. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the
mean number of books checked out each day. The assistant provides the following interval
estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the
number of books checked out each day at the Library of Congress?
a) 740
b) 830
c) 920
d) 1,660
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: point estimate, mean
32. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the
mean number of books checked out each day. The assistant provides the following interval
estimate: from 740 to 920 books per day. If the head librarian knows that the population standard
deviation is 150 books checked out per day, approximately how large a sample did her assistant
use to determine the interval estimate?
a) 2
b) 3
c) 12
d) It cannot be determined from the information given.
ANSWER:
d
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: mean, sample size determination Confidence Interval Estimation205
33. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the
mean number of books checked out each day. The assistant provides the following interval
estimate: from 740 to 920 books per day. If the head librarian knows that the population standard
deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence
interval, approximately how large a sample did her assistant use to determine the interval estimate?
a) 125
b) 13
c) 11
d) 4
ANSWER:
c
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: mean, sample size determination
34. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the
mean number of books checked out each day. The assistant provides the following interval
estimate: from 740 to 920 books per day. If the head librarian knows that the population standard
deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to
construct the interval estimate, what confidence level can she attach to the interval estimate?
a) 99.7%
b) 99.0%
c) 98.0%
d) 95.4%
ANSWER:
a
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: mean, sample size determination
35. True or False: A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained
an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval
for the 0 to 60 time is 4.52 seconds to 5.18 seconds.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution
36. True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7, a 90%
confidence interval will have a width of 2.36.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution 206 Confidence Interval Estimation
37. True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7, a 90%
confidence interval will have a width of 2.36.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, standardized normal distribution
38. True or False: A sample size of 5 provides a sample mean of 9.6. If the population variance is
known to be 5 and the population distribution is assumed to be normal, the lower limit for a 92%
confidence interval is 7.85.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, standardized normal distribution
39.True or False: A random sample of 50 provides a sample mean of 31 with a standard deviation of
s=14. The upper bound of a 90% confidence interval estimate of the population mean is 34.32.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, mean, t distribution
40.True or False: In forming a 90% confidence interval for a population mean from a sample size of
22, the number of degrees of freedomfrom the t distribution equals 22.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
41. True or False: Other things being equal, as the confidence level for a confidence interval increases,
the width of the interval increases.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, properties
42.True or False: The t distribution allows the calculation of confidence intervals for means when the
actual standard error is not known.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
43.True or False: The t distribution allows the calculation of confidence intervals for means for small
samples when the population variance is not known, regardless of the shape of the distribution in
the population. Confidence Interval Estimatio207
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
44. True or False: For a t distribution with 12 degrees of freedom, the area between – 2.6810 and
2.1788 is 0.980.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: t distribution
45. True or False: A sample of 100 fuses from a very large shipment is found to have 10 that are
defective. The 0.95 confidence interval would indicate that, for this shipment, the proportion of
defective fuses is between 0 and 0.28.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, proportion
46. True or False: The sample mean is a point estimate of the population mean.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: point estimate, mean
47. True or False: The confidence interval estimate of the population mean is constructed around the
sample mean.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean
48. True or False: The confidence interval estimate of the population proportion is constructed around
the sample proportion.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, proportion 208 Confidence Interval Estimation
49. True or False: A point estimate consists of a single sample statistic that is used to estimate the true
population parameter.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: point estimate
50. True or False: The confidence interval obtained will always correctly estimate the population
parameter.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, interpretation
51. True or False: Other things being equal, the confidence interval for the mean will be wider for 95%
confidence than for 90% confidence.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, properties, width
52.True or False: The t distribution is used to develop a confidence interval estimate of the population
mean when the population standard deviation is unknown.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
53.True or False: The t distribution is used to develop a confidence interval estimate of the population
proportion when the population standard deviation is unknown.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, proportion, t distribution
54. True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion regardless of whether the population standard deviation is
known.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, proportion, standardized normal distribution Confidence Interval Estimatio209
55. True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion when the sample size is sufficiently large.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, proportion, standardized normal distribution
56. True or False: The t distribution approaches the standardized normal distribution when the number
of degrees of freedomincreases.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: t distribution, standardized normal distribution
57. True or False: In estimating the population mean with the population standard deviation unknown,
if the sample size is 12, there will be 6 degrees of freedom.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: confidence interval, mean, t distribution
58. True or False: The difference between the sample mean and the population mean is called the
sampling error.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
59. True or False: The difference between the sample proportion and the population proportion is
called the sampling error.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
60. True or False: The difference between the sample size and the population size is called the
sampling error.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling error 210 Confidence Interval Estimation
61. True or False: The difference between the upper limit of a confidence interval and the point
estimate used in constructing the confidence interval is called the sampling error.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
62. True or False: The difference between the lower limit of a confidence interval and the point
estimate used in constructing the confidence interval is called the sampling error.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
63. True or False: Sampling error equals to half the width of a confidence interval.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
64. True or False: The width of a confidence interval equals twice the sampling error.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling error
65. True or False: The sampling error can either be positive or negative.
ANSWER:
True
TYPE: TF DIFFICULTY: Difficult
KEYWORDS: sampling error
66. True or False: A population parameter is used to estimate a confidence interval.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: point estimate, confidence interval Confidence Interval Estimation211
67. True or False: For a given data set and confidence level, the confid

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