Interval Estimation 1
Chapter Eight
In the following multiple choice questions, circle the correct answer.
1.The absolute value of the difference between the point estimate and the population parameter it estimates is the
a.standard error
b.sampling error
c.precision
d.error of confidence
e.None of the above answers is correct.
ANSWER:b
2.The confidence associated with an interval estimate is called the
a.significance
b.degree of association
c.confidence level
d.precision
e.None of the above answers is correct.
ANSWER:c
3.A probability statement about the sampling error is known as the
a.confidence
b.precision
c.interval
d.error
e.None of the above answers is correct.
ANSWER:b
4.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
e.None of the above answers is correct.
ANSWER:c
5.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 above answers is correct.
ANSWER:b
6.For the interval estimation of when is known and the sample is large, the proper distribution to use is
a.the normal distribution
b.the t distribution with n degrees of freedom
c.the t distribution with n - 1 degrees of freedom
d.the t distribution with n - 2 degrees of freedom
e.None of the above answers is correct.
ANSWER:a
7.The variance of a population is known to be 400. At 95% confidence, the margin of error will be
a.39.2 or less
b.3.92 or less
c.3.29 or less
d.78.4 or less
e.None of the above answers is correct.
ANSWER:b
8.An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
a.confidence level
b.interval estimate
c.parameter value
d.population estimate
e.None of the above answers is correct.
ANSWER:b
9.The difference between the point estimate, such as the sample mean, and the value of the population parameter it estimates, such as the population mean, is known as the
a.confidence level
b.sampling error
c.parameter estimate
d.interval estimate
e.None of the above answers is correct.
ANSWER:b
10.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
e.None of the above answers is correct.
ANSWER:c
11.Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?
a.standard distribution
b.z distribution
c.beta distribution
d.t distribution
e.None of the above answers is correct.
ANSWER:d
12.In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.2 hours. The standard error of the mean is
a.7.5
b.0.014
c.0.160
d.0.133
ANSWER:d
13.In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.2 hours. With a 0.95 probability, the margin of error is approximately
a.0.26
b.1.96
c.0.21
d.1.64
ANSWER:a
14.In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.2 hours. If the sample mean is 9 hours, then the 95% confidence interval is
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
ANSWER:d
15.The t distribution is applicable whenever
a.the sample is considered large (n 30).
b.the population is normal and the sample standard deviation is used to estimate the population standard deviation
c.both a and b
d.None of the above answers is correct.
ANSWER:b
16.In developing an interval estimate, if the population standard deviation is unknown
a.it is impossible to develop an interval estimate
b.the standard deviation is arrived at using historical data
c.the sample standard deviation can be used
d.None of the above answers is correct.
ANSWER:c
17.In order to use the normal distribution for interval estimation of when is known, the population
a.must be very large
b.must have a normal distribution
c.can have any distribution
d.None of the above answers is correct.
ANSWER:b
18.From a population which is not normally distributed and whose standard deviation is not known, a sample of 20 items is selected to develop an interval estimate for .
a.The normal distribution can be used.
b.The t distribution with 19 degrees of freedom must be used.
c.The t distribution with 20 degrees of freedom must be used.
d.The sample size must be increased.
e.None of the above answers is correct.
ANSWER:d
19.A sample of 100 elements from a population is selected, and the standard deviation of the sample is computed. For an interval estimation of , the proper distribution to use is the
a.normal distribution
b.t distribution with 100 degrees of freedom
c.t distribution with 99 degrees of freedom
d.None of the above answers is correct.
ANSWER:a
20.From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of , the proper distribution to use is the
a.normal distribution
b.t distribution
c.t distribution with 26 degrees of freedom
d.t distribution with 24 degrees of freedom
e.None of the above answers is correct.
ANSWER:d
21.The z value for a 97.8% confidence interval estimation is
a.2.02
b.1.96
c.2.00
d.2.29
e.None of the above answers is correct.
ANSWER:d
22.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
e.None of the above answers is correct.
ANSWER:b
23.As the sample size increases, the sampling error
a.increases
b.decreases
c.stays the same
d.None of the above answers is correct.
ANSWER:b
24.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 = 0.01
d.P = 0.50
e.None of the above answers is correct.
ANSWER:d
25.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
e.None of the above answers is correct.
ANSWER:a
26.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.
e.None of the above answers is correct.
ANSWER:b
27.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 above answers is correct.
ANSWER:a
28.After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
a.Increase the level of confidence for the interval.
b.Discard the current data and try a different sample.
c.Increase the sample size.
d.Reduce the population variance.
e.None of the above answers is correct.
ANSWER:c
29.If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect
a.the size of the confidence interval to increase
b.the size of the confidence interval to decrease
c.the size of the confidence interval to remain the same
d.the sample size to increase
e.None of the above answers is correct.
ANSWER:a
30.In general, higher confidence levels provide
a.wider confidence intervals
b.narrower confidence intervals
c.a smaller standard error
d.unbiased estimates
e.None of the above answers is correct.
ANSWER:a
31.An interval estimate is a range of values used to estimate
a.the shape of the population's distribution
b.the sampling distribution
c.a sample statistic
d.a population parameter
e.None of the above answers is correct.
ANSWER:d
32.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
e.None of the above answers is correct.
ANSWER:d
33.Whenever using the t distribution in estimation, we must assume that
a.the sample size is at least 30
b.the sampling distribution is approximately normal
c.the population is approximately normal
d.the finite population correction factor is necessary
e.None of the above answers is correct.
ANSWER:c
34.A sample of 20 items from a population with an unknown is selected in order to develop an interval estimate of . Which of the following is not necessary?
a.We must assume the population has a normal distribution.
b.We must use a t distribution.
c.Sample standard deviation must be used to estimate .
d.The sample must have a normal distribution.
e.All of the above are necessary.
ANSWER:d
35.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
e.None of the above answers is correct.
ANSWER:a
36.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
e.None of the above answers is correct.
ANSWER:b
37.Which of the following best describes the form of the sampling distribution of the sample proportion?
a.When standardized, it is exactly the standard normal distribution.
b.When standardized, it is the t distribution.
c.It is approximately normal as long as n 30.
d.It is approximately normal as long as np 5 and
n(1-p) 5.
e.None of the above answers is correct.
ANSWER:d
38.In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is
a.0.122 to 0.278
b.0.164 to 0.236
c.0.134 to 0.266
d.0.120 to 0.280
e.None of the above answers is correct.
ANSWER:d
39.We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?
a.200
b.100
c.58
d.196
e.None of the above answers is correct.
ANSWER:c
40.In a sample of 500 voters, 400 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
a.0.782 to 0.818
b.0.120 to 0.280
c.0.765 to 0.835
d.0.165 to 0.235
e.0.2 to 0.8
ANSWER:d