Deck 8: Interval Estimation

Question 1

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.

A) .1
B) .95
C) .9
D) .05

Answer 1

.9

Question 2

The expression used to compute an interval estimate of μ 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

Answer 2

whether there is sampling error

Question 3

In determining an interval estimate of a population mean when ? is unknown, we use a t distribution with _____ degrees of freedom.

A) $\sqrt { n - 1 }$
B) $\sqrt { n }$
C) n ? 1
D) n

Answer 3

n ? 1

Question 4

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 μ
D) None of the answers is correct.

Question 5

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

A) uniform
B) normal
C) exponential
D) p

Question 6

As the sample size increases, the margin of error _____.

A) increases
B) decreases
C) stays the same
D) None of the answers is correct.

Question 7

For the interval estimation of μ when σ 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

Question 8

The mean of the t distribution is _____.

A) 0
B) .5
C) 1
D) dependent upon the sample size

Question 9

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____.

A) .485
B) 1.96
C) .95
D) 1.645

Question 10

The use of the normal probability distribution as an approximation of the sampling distribution of $\bar { p }$ is based on the condition that both np and n(1 - p) equal or exceed _____.

A) .05
B) 5
C) 15
D) 30

Question 11

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

Question 12

The z value for a 97.8% confidence interval estimation is _____.

A) 2.02
B) 1.96
C) 2.00
D) 2.29

Question 13

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

Question 14

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

Question 15

If the margin of error in an interval estimate of ? is 4.6, the interval estimate equals _____.

A) $\bar { x } \pm 2.3$
B) $\bar { x } \pm 4.6$
C) $\bar { x } \pm 4.508$
D) $\bar { x } \pm 6.9$

Question 16

The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.

A) level of significance
B) confidence level
C) confidence coefficient
D) error factor

Question 17

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, 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

Question 18

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

Question 19

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) using a planning value p* closer to .5
C) increasing the level of significance
D) reducing the confidence coefficient

Question 20

The confidence associated with an interval estimate is called the _____.

A) level of significance
B) degree of association
C) confidence level
D) precision

Question 21

From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, 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

Question 22

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____.

A) becomes narrower
B) becomes wider
C) does not change
D) becomes .1

Question 23

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

Question 24

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.NORM
B) NORM.INV
C) T.INV
D) INT

Question 25

Whenever using the t distribution in interval estimation, we must assume that _____.

A) the sample size is less than 30
B) a random sample was selected
C) the population is approximately normal
D) the finite population correction factor is necessary

Question 26

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 answers is correct.

Question 27

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 μ 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

Question 28

When the level of confidence increases, the confidence interval _____.

A) stays the same
B) becomes wider
C) becomes narrower
D) cannot be determined from the information given

Question 29

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

Question 30

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

Question 31

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 selected. The population standard deviation is known. Which Excel function would NOT be appropriate to use to construct a confidence interval estimate?

A) NORM.S.INV
B) COUNTIF
C) AVERAGE
D) STDEV

Question 32

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

Question 33

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 answers is correct.

Question 34

It is known that the variance of a population equals 1,936. A random sample of 121 has been selected 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

Question 35

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.

Question 36

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 μ. 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.

Question 37

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

Question 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 answers is correct.

Question 39

In general, higher confidence levels provide _____.

A) wider confidence intervals
B) narrower confidence intervals
C) a smaller standard error
D) unbiased estimates

Question 40

A random sample of 25 statistics examinations was selected. 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) 69.29 to 82.71

Question 41

A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random sample of 50 items is selected. Which Excel function would NOT be appropriate to construct a confidence interval estimate?

A) NORM.S.INV
B) COUNTIF
C) STDEV
D) All of these answers are correct.

Question 42

A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Provide a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile of campus. Assume this population is normally distributed.

Question 43

In determining the sample size necessary to estimate a population proportion, which of the following 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

Question 44

Below you are given ages that were obtained by taking a random sample of nine undergraduate students.
19
22
23
19
21
22
19
23
21
Use Excel to determine an interval estimate for the mean of the population at a 99% confidence level. Interpret your results.

Question 45

It is known that the population variance equals 484. With a .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

Question 46

Using α = .04, a confidence interval for a population proportion is determined to be .65 to .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.

Question 47

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

A) uniform
B) normal
C) exponential
D) p

Question 48

The degrees of freedom associated with a t distribution are a function of the _____.

A) area in the upper tail
B) sample standard deviation
C) confidence coefficient
D) sample size

Question 49

For which of the following values of p is the value of P(1 − p) maximized?

A) p = .99
B) p = .90
C) p = 1.0
D) p = .50

Question 50

If the margin of error in an interval estimate of ? is 4.6, the interval estimate equals _____.

A) $\bar { x } \pm 2.3$
B) $\bar { x } \pm 4.6$
C) $\bar { x } \pm 4.508$
D) $\bar { x } \pm 6.9$

Question 51

A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of five examinations is selected at random and scored. The scores are shown below. Use Excel to determine an interval estimate for the mean of the population at a 98% confidence level. Interpret your results.

Question 52

A marketing firm is developing a new television advertisement for a large discount retail chain. A sample of 30 people is shown two potential ads and asked their preference. The results for ad #1 follow. Use Excel to develop a 95% confidence interval estimate of the proportion of people in the population who will prefer ad #1.

Question 53

A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is selected. 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) NORM.S.INV
B) NORM.INV
C) T.INV
D) INT

Question 54

Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for $\bar{p}$ . In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size for a given level of confidence and a given margin of error is

A) .10
B) .50
C) .90
D) 1

Question 55

A survey of 40 students at a local college asks, "Where do you buy the majority of your books?" The responses fell into three categories: "at the campus bookstore," "on the Internet," and "other." The results follow. Use Excel to estimate the proportion of the college students who buy their books on the Internet.

Question 56

A random sample of 36 magazine subscribers is selected to estimate the mean age of all subscribers. The data follow. Use Excel to construct a 90% confidence interval estimate of the mean age of all of this magazine's subscribers.

Question 57

The general form of an interval estimate of a population mean or population proportion is the _____ plus or minus the _____.

A) population mean, standard error
B) level of significance, degrees of freedom
C) point estimate, margin of error
D) planning value, confidence coefficient

Question 58

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

Question 59

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) np ≥ 5 and n(1 − p) ≥ 5

Question 60

The margin of error in an interval estimate of the population mean is a function of all of the following EXCEPT _____.

A) level of significance
B) sample mean
C) sample size
D) variability of the population

Question 61

The mean of the t distribution is _____.

A) 0
B) .5
C) 1
D) dependent upon the sample size

Question 62

It is known that the variance of a population equals 1,936. A random sample of 121 has been selected 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

Question 63

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

Question 64

In determining an interval estimate of a population mean when ? is unknown, we use a t distribution with _____ degrees of freedom.

A) $\sqrt { n - 1 }$
B) $\sqrt { n }$
C) n ? 1
D) n

Question 65

The z value for a 97.8% confidence interval estimation is _____.

A) 2.02
B) 1.96
C) 2.00
D) 2.29

Question 66

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____.

A) .485
B) 1.96
C) .95
D) 1.645

Question 67

The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.

A) level of significance
B) confidence level
C) confidence coefficient
D) error factor

Question 68

As the sample size increases, the margin of error _____.

A) increases
B) decreases
C) stays the same
D) None of the answers is correct.

Question 69

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) using a planning value p* closer to .5
C) increasing the level of significance
D) reducing the confidence coefficient

Question 70

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.

A) .1
B) .95
C) .9
D) .05

Question 71

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

Question 72

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

Question 73

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 μ
D) None of the answers is correct.

Question 74

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

Question 75

The use of the normal probability distribution as an approximation of the sampling distribution of $\bar { p }$ is based on the condition that both np and n(1 - p) equal or exceed _____.

A) .05
B) 5
C) 15
D) 30

Question 76

For the interval estimation of μ when σ 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

Question 77

The expression used to compute an interval estimate of μ 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

Question 78

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

Question 79

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, 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

Question 80

The confidence associated with an interval estimate is called the _____.

A) level of significance
B) degree of association
C) confidence level
D) precision