Deck 8: Interval Estimation

Question 1

An estimator is unbiased if its expected value equals the estimated population parameter.

Answer 1

True

Question 2

An estimator is consistent if it approaches the estimated population parameter as the sample size grows larger.

Answer 2

True

Question 3

A point estimate is a function of the random sample used to make inferences about the value of an unknown population parameter.A point estimator reflects the actual value of the point estimate derived from a given sample.

Answer 3

False

Question 4

A confidence interval provides a value that,with a certain measure of confidence,is the population parameter of interest.

Question 5

If a random sample of size n is taken from a normal population with a finite variance,then the statistic follows the t distribution with (n - 1)degrees of freedom,df.

Question 6

How is the unbiasness of estimators defined?

A)An estimator is unbiased if its expected value equals the estimated population parameter.
B)An unbiased estimator approaches the estimated population parameter as the sample size grows larger.
C)An estimator is unbiased if it always gives the correct value of the estimated population parameter.
D)An estimator is unbiased if its standard error is lower than that of other estimators of the estimated population parameter.

Question 7

For a given sample size n and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the confidence level .

Question 8

Which of the following is a point estimate?

A)
B)P
C)μ
D)

Question 9

For a given confidence level and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the sample size n.

Question 10

How is the consistency of estimators defined?

A)An estimator is consistent if its expected value equals the estimated population parameter.
B)A consistent estimator approaches the estimated population parameter as the sample size grows larger.
C)An estimator is consistent if it always gives the correct value of the estimated population parameter.
D)An unbiased estimator is consistent if its standard error is lower than that of other estimators of the estimated population parameter.

Question 11

An unbiased estimator is efficient if its standard error is higher than that of other unbiased estimators of the estimated population parameter.

Question 12

For a given confidence level and sample size n,the width of the confidence interval for the population mean is narrower,the greater the population standard deviation σ.

Question 13

Like the z distribution,the t distribution is symmetric around 0,bell-shaped,and with tails that approach the horizontal axis and eventually cross it.

Question 14

An estimator that tends to produce more accurate estimates of the population parameter as the sample size increases is best characterized as a(n)____________.

A)Biased estimator
B)Efficient estimator
C)Unbiased estimator
D)Consistent estimator

Question 15

How does an interval estimator differ from a point estimator?

A)A point estimator may produce very biased results,while an interval estimator never has such a feature.
B)If a point estimator fails to produce an unbiased result,then an interval estimator secures such a result.
C)An interval estimator provides a range of values that always include the estimated population parameter.
D)An interval estimator provides a range of values for the estimated population parameter rather than a single value provided by a point estimator.

Question 16

Which of the following is a point estimator?

A)
B)p
C)
D)

Question 17

How is the efficiency of estimators defined?

A)An estimator is efficient if its expected value equals the estimated population parameter.
B)An efficient estimator approaches the estimated population parameter as the sample size grows larger.
C)An estimator is efficient if it always gives the correct value of the estimated population parameter.
D)An unbiased estimator is efficient if its standard error is lower than that of other estimators of the estimated population parameter.

Question 18

The t distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom,df.For lower values of df,the t distribution is similar to the z distribution.

Question 19

The t distribution has broader tails than the z distribution.

Question 20

If we want to find the required sample size for the interval estimation of the population proportion,and no reasonable estimate of this proportion is available,we assume the worst-case scenario under which .

Question 21

An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year.Holding all else constant,if he increased the sample size to 30 firms,how are the standard error of the mean and the width of the confidence interval affected?

A)Option A
B)Option B
C)Option C
D)Option D

Question 22

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120.The revenue on each of the last 25 days is noted,and the average is computed as $550.Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor.

A)
B)
C)
D)

Question 23

Which of the following is the necessary condition for creating confidence intervals for the population mean?

A)Normality of the estimator
B)Normality of the population
C)Known population parameter
D)Known standard deviation of the estimator

Question 24

For a given sample size and population standard deviation,which of the following is true in the interval estimation of the population mean?

A)If the confidence level is greater,the interval is wider.
B)If the confidence level is smaller,the interval is wider.
C)If the confidence level is greater,the interval is narrower.
D)No answer choices are correct.

Question 25

For a given confidence level and population standard deviation,which of the following is true in the interval estimation of the population mean?

A)If the sample size is greater,the interval is narrower.
B)If the sample size is smaller,the interval is narrower.
C)If the population size is greater,the interval is narrower.
D)If the population size is smaller,the interval is narrower.

Question 26

What is for a 90% confidence interval of the population mean?

A)0.48
B)0.49
C)1.645
D)1.96

Question 27

In an examination of purchasing patterns of shoppers,a sample of 16 shoppers revealed that they spent,on average,$54 per hour of shopping.Based on previous years,the population standard deviation is thought to be $21 per hour of shopping.Assuming that the amount spent per hour of shopping is normally distributed,find a 90% confidence interval for the mean amount.

A)[45.3637,62.6363]
B)[47.2695,60.7305]
C)[51.8409,56.1591]
D)[52.3174,55.6826]

Question 28

Exhibit 8.1.The ages of MBA students at a university are normally distributed with a known population variance of 10.24.Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. Refer to Exhibit 8.1.If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean,then _____________.

A)The resulting margin of error will increase and the risk of reporting an incorrect interval will increase
B)The resulting margin of error will decrease and the risk of reporting an incorrect interval will increase
C)The resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
D)The resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

Question 29

What is for a 95% confidence interval of the population mean?

A)0.48
B)0.49
C)1.645
D)1.96

Question 30

At a particular academically challenging high school,the average GPA of a high school senior is known to be normally distributed with a variance of 0.25.A sample of 20 seniors is taken and their average GPA is found to be 2.71.Develop a 90% confidence interval for the population mean GPA.

A)[2.5261,2.8939]
B)[2.5667,2.8533]
C)[2.6180,2.8020]
D)[2.6384,2.7816]

Question 31

A 90% confidence interval is constructed for the population mean.If a 95% confidence interval had been constructed instead (everything else remaining the same),the width of the interval would have been ________ and the probability of making an error would have been _________.

A)Wider;bigger
B)Wider;smaller
C)Narrower;bigger
D)Narrower;smaller

Question 32

We draw a random sample of size 25 from the normal population with the variance 2.4.If the sample mean is 12.5,what is a 99% confidence interval for the population mean?

A)[11.2600,13.7400]
B)[11.3835,13.6165]
C)[11.7019,13.2981]
D)[11.7793,13.2207]

Question 33

Exhibit 8.1.The ages of MBA students at a university are normally distributed with a known population variance of 10.24.Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. Refer to Exhibit 8.1.What is the margin of error for a 95% confidence interval for the population mean?

A)1.645(3.20/6)
B)1.645(10.24/6)
C)1.96(3.20/6)
D)1.96(10.24/6)

Question 34

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120.The revenue on each of the last 25 days is noted,and the average is computed as $550.A 95% confidence interval is constructed for the population mean revenue.If the data from the last 40 days had been used,then the resulting 95% confidence intervals would have been _____________________.

A)Wider,with a larger probability of reporting an incorrect interval
B)Wider,with the same probability of reporting an incorrect interval
C)Narrower,with a larger probability of reporting an incorrect interval
D)Narrower,with the same probability of reporting an incorrect interval

Question 35

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation.If a bigger sample had been used instead,then the 95% confidence interval would have been _______ and the probability of making an error would have been ________.

A)Wider,smaller
B)Narrower,smaller
C)Wider,unchanged
D)Narrower,unchanged

Question 36

What is the purpose of calculating a confidence interval?

A)To provide a range of values that has a certain large probability of containing the sample statistic of interest
B)To provide a range of values that,with a certain measure of confidence,contains the sample statistic of interest
C)To provide a range of values that,with a certain measure of confidence,contains the population parameter of interest
D)To provide a range of values that has a certain large probability of containing the population parameter of interest

Question 37

What is the most typical form of a calculated confidence interval?

A)Point estimate ± Standard error
B)Point estimate ± Margin of error
C)Population parameter ± Standard error
D)Population parameter ± Margin of error

Question 38

Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50.The last seven times John has taken a taxi from Logan to downtown Boston the fares have been $22.10,$23.25,$21.35,$24.50,$21.90,$20.75,and $22.65.What is a 95% confidence interval for the population mean taxi fare?

A)[$17.4571,$27.2571]
B)[$20.5051,$24.2091]
C)[$20.8027,$23.9115]
D)[$21.6571,$23.0571]

Question 39

For a given confidence level and sample size,which of the following is true in the interval estimation of the population mean when σ is known?

A)If the sample standard deviation is smaller,the interval is wider.
B)If the population standard deviation is greater,the interval is wider.
C)If the population standard deviation is smaller,the interval is wider.
D)If the population standard deviation is greater,the interval is narrower.

Question 40

We draw a random sample of size 36 from a population with the standard deviation 3.5.If the sample mean is 27,what is a 95% confidence interval for the population mean?

A)[25.8567,28.1433]
B)[26.0405,27.9595]
C)[26.8100,27.1900]
D)[26.8401,27.1599]

Question 41

Given a sample mean of 12.5-drawn from a normal population,a sample of size 25,and a sample variance of 2.4-find a 99% confidence interval for the population mean.

A)[11.7019,13.2981]
B)[11.1574,13.8426]
C)[11.6334,13.3666]
D)[11.7279,13.2721]

Question 42

Exhibit 8-3.Professors of Accountancy are in high demand at American universities.A random sample of 28 new accounting professors found the average salary was 135 thousand dollars with a standard deviation of 16 thousand dollars.Assume the distribution is normally distributed. Refer to Exhibit 8-3.Construct a 95% confidence interval for the salary of new accounting professors.Answers are in thousands of dollars.

A)[102.1680,167.832]
B)[127.8247,142.1753]
C)[128.7953,141.2047]
D)[129.0735,140.9265]

Question 43

The confidence intervals for the population proportion are generally based on ___________.

A)The z distribution
B)The t distribution
C)The z distribution when the sample size is very small
D)The t distribution when the population standard deviation is not known

Question 44

What is for a 99% confidence interval of the population mean based on a sample of 25 observations?

A)2.492
B)2.576
C)2.787
D)2.797

Question 45

What is for a 95% confidence interval of the population mean based on a sample of 15 observations?

A)1.761
B)1.960
C)2.131
D)2.145

Question 46

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown.How are these two cases treated differently?

A)Use the z table when s is unknown;use the t table when s is known.
B)Use the z table when s is known;use the t table when s is unknown.
C)Use the z table when σ is unknown;use the t table when σ is known.
D)Use the z table when σ is known;use the t table when σ is unknown.

Question 47

What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?

A)The underlying population must be normally distributed.
B)The underlying population must be normally distributed if the sample size is 30 or more.
C)The underlying population need not be normally distributed if the sample size is 30 or more.
D)The underlying population need not be normally distributed if the population standard deviation is known.

Question 48

Exhibit 8-2.The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S.economy in many ways,but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure,and lenders became more wary of filing faulty documentation.Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed,transferring the property)has been 230 days,420 days,340 days,367 days,295 days,314 days,385 days,and 311 days.Assume the duration is normally distributed. Refer to Exhibit 8-2.Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.

A)[126.2730,539.2270]
B)[259.7486,405.7514]
C)[279.0056,386.4944]
D)[291.8600,373.6400]

Question 49

At a particular academically challenging high school,the average GPA of a high school senior is known to be normally distributed.After a sample of 20 seniors is taken,the average GPA is found to be 2.71 and the variance is determined to be 0.25.Find a 90% confidence interval for the population mean GPA.

A)[2.5167,2.9033]
B)[2.5261,2.3939]
C)[2.5615,2.8585]
D)[2.6358,2.7842]

Question 50

Exhibit 8-3.Professors of Accountancy are in high demand at American universities.A random sample of 28 new accounting professors found the average salary was 135 thousand dollars with a standard deviation of 16 thousand dollars.Assume the distribution is normally distributed. Refer to Exhibit 8-3.Construct a 90% confidence interval for the salary of new accounting professors.Answers are in thousands of dollars.

A)[107.7520,162.2480]
B)[129.8506,140.1494]
C)[130.0260,139.9740]
D)[131.0268,138.9732]

Question 51

Exhibit 8-2.The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S.economy in many ways,but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure,and lenders became more wary of filing faulty documentation.Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed,transferring the property)has been 230 days,420 days,340 days,367 days,295 days,314 days,385 days,and 311 days.Assume the duration is normally distributed. Refer to Exhibit 8-2.Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston.

A)[259.7400,405.7600]
B)[293.2137,372.2863]
C)[298.4296,367.0704]
D)[303.2282,362.2718]

Question 52

A company that produces computers recently tested the battery in its latest laptop in six separate trials.The battery lasted 8.23,7.89,8.14,8.25,8.30,and 7.95 hours before burning out in each of the tests.Assuming the battery duration is normally distributed,construct a 95% confidence interval for the mean battery life in the new model.

A)[7.9489,8.3045]
B)[7.9575,8.2959]
C)[7.9873,8.2661]
D)[7.9912,8.2622]

Question 53

Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36,find a 95% confidence interval on the population mean.

A)[25.8158,28.1842]
B)[25.8170,28.1830]
C)[26.0142,27.9858]
D)[26.9930,27.0070]

Question 54

The GPA of accounting students in a university is known to be normally distributed.A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16.Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

A)
B)
C)
D)

Question 55

The starting salary of business students in a university is known to be normally distributed.A random sample of 18 business students results in a mean salary of $46,500 with a standard deviation of $10,200.Construct the 90% confidence interval for the mean starting salary of business students in this university.

A)
B)
C)
D)

Question 56

A website advertises job openings on its website,but job seekers have to pay to access the list of job openings.The website recently completed a survey to estimate the number of days it takes to find a new job using their service.It took the last 30 customers an average of 60 days to find a job.Assume the population standard deviation is 10 days.Calculate a 95% confidence interval of the population mean number of days it takes to find a job.

A)[40.4000,79.6000]
B)[55.9085,64.0915]
C)[56.4215,63.5785]
D)[56.9966,63.0034]

Question 57

In an examination of holiday spending (known to be normally distributed)of a sample of 16 holiday shoppers at a local mall,an average of $54 was spent per hour of shopping.Based on the current sample,the standard deviation is equal to $21.Find a 90% confidence interval for the population mean level of spending per hour.

A)[$44.8335,$63.1665]
B)[$44.7967,$63.2033]
C)[$45.3637,$62.6363]
D)[$46.9597,$61.0403]

Question 58

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice.The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35.Construct a 99% confidence interval for the average number of free throws in practice.

A)[210.5995,239.4005]
B)[210.6155,239.3845]
C)[211.2506,238.7494]
D)[214.2290,235.7710]

Question 59

The t distribution is similar to the z distribution because _________________.

A)As the degrees of freedom go to infinity,the t distribution converges to the z distribution
B)Both have asymptotic tails-that is,their tails become closer and closer to the horizontal axis,but never touch it
C)Both A and B are correct
D)Neither A nor B is correct

Question 60

How do the t and z distributions differ?

A)There is no difference between the t and z distributions.
B)The z distribution has broader tails (it is flatter around zero).
C)The t distribution has broader tails (it is flatter around zero).
D)The z distribution has asymptotic tails,while the t distribution does not.

Question 61

Statisticians like precision in their interval estimates.A low margin of error is needed to achieve this.Which of the following supports this when selecting sample sizes?

A)A larger sample size reduces the margin of error.
B)A smaller sample size reduces the margin of error.
C)A larger sample size increases the margin of error.
D)A sample size has no impact on the margin of error.

Question 62

Exhibit 8.4.According to a report in USA Today (February 1,2012),more and more parents are helping their young adult children get homes.Suppose 8 persons in a random sample of 40 young adults who recently purchased a home in Kentucky got help from their parents.You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who got help from their parents. Refer to Exhibit 8.4.What is the margin of error for a 95% confidence interval for the population proportion?

A)1.645(0.0040)
B)1.645(0.0632)
C)1.96(0.0040)
D)1.96(0.0632)

Question 63

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election.Candidate A is facing two opposing candidates.In a preselected poll of 100 residents,22 supported her.The desired margin of error is 0.08.

A)n = 44
B)n = 72
C)n = 73
D)n = 103

Question 64

Exhibit 8-6.A sample of 1400 American households was asked if they planned to buy a new car next year.Of the respondents,34% indicated they planned to buy a new car next year. Refer to Exhibit 8-6.Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.

A)[0.3074,0.3726]
B)[0.3105,0.3695]
C)[0.3140,0.3660]
D)[0.3392,0.3408]

Question 65

Exhibit 8-5.A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents indicating "unfriendly" and 6% of respondents indicating "an enemy" (Gallup,Nov.30 - Dec.18,2011). Refer to Exhibit 8-5.Construct a 95% confidence interval of the proportion of American adults who view China as either "unfriendly" or as "an enemy."

A)[0.2013,0.2587]
B)[0.2116,0.2484]
C)[0.2146,0.2454]
D)[0.2208,0.2392]

Question 66

Construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election.Candidate A is facing two opposing candidates in a mayoral election.In a recent poll of 300 residents,she has garnered 51% support.

A)[0.4534,0.5666]
B)[0.4625,0.5575]
C)[0.5084,0.5116]
D)[0.5086,0.5114]

Question 67

Exhibit 8-5.A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents indicating "unfriendly" and 6% of respondents indicating "an enemy" (Gallup,Nov.30 - Dec.18,2011). Refer to Exhibit 8-5.Construct a 99% confidence interval of the proportion of American adults who view China as "an enemy."

A)[0.0463,0.0737]
B)[0.0476,0.0724]
C)[0.0512,0.0688]
D)[0.0597,0.0603]

Question 68

A medical devices company wants to know the number of hours their MRI machines are used per day.A previous study found a standard deviation of four hours.How many MRI machines must the company find data for in order to have a margin of error of at most 0.5 hours when calculating a 98% confidence interval?

A)346.26
B)347
C)424.69
D)425

Question 69

Which of the following is the correct formula for the margin of error in the interval estimation of p?

A)
B)
C)
D)

Question 70

Exhibit 8-6.A sample of 1400 American households was asked if they planned to buy a new car next year.Of the respondents,34% indicated they planned to buy a new car next year. Refer to Exhibit 8-6.Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year.

A)[0.3152,0.3648]
B)[0.3191,0.3609]
C)[0.3394,0.3406]
D)[0.3354,0.3446]

Question 71

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198.Which of the following is the approximate value of the assumed estimate of the population standard deviation?

A)10.7688
B)12.8309
C)115.9671
D)164.6326

Question 72

Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error.If there is no rough estimate of the population proportion,what value should be assumed for ?

A)0.05
B)0.10
C)0.50
D)0.90

Question 73

A marketing firm wants to estimate how much root beer the average teenager drinks per year.A previous study found a standard deviation of 1.12 liters.How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liters when constructing a 99% confidence interval?

A)29
B)832
C)832.39
D)833

Question 74

When examining the possible outcome of an election,what type of confidence interval is most suitable for estimating the current support for a candidate?

A)The confidence interval for the sample mean
B)The confidence interval for the population mean
C)The confidence interval for the sample proportion
D)The confidence interval for the population proportion

Question 75

When the required sample size calculated by using a formula is not a whole number,what is the best choice for the required sample size?

A)Round the result of the calculation in a standard way.
B)Round the result of the calculation up to the nearest whole number.
C)Round the result of the calculation down to the nearest whole number.
D)None of the above.

Question 76

The sampling distribution of the population proportion is based on a binomial distribution.What condition must be met to use the normal approximation for the confidence interval?

A)n ≥ 30
B)
C)
D)

Question 77

Construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election.Candidate A is facing two opposing candidates.In a recent poll of 300 residents,153 supported her.

A)[0.4534,0.5666]
B)[0.4625,0.5575]
C)[0.5086,0.5114]
D)[0.5090,0.5110]

Question 78

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D = 1.25? The standard deviation in a preselected sample is 8.5.

A)n = 76
B)n = 125
C)n = 126
D)n = 190

Question 79

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is D = 1.5? The population standard deviation is known to be 10.75.

A)n = 138
B)n = 139
C)n = 197
D)n = 198

Question 80

Exhibit 8.4.According to a report in USA Today (February 1,2012),more and more parents are helping their young adult children get homes.Suppose 8 persons in a random sample of 40 young adults who recently purchased a home in Kentucky got help from their parents.You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who got help from their parents. Refer to Exhibit 8.4.If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion,then ____________________.

A)The resulting margin of error will increase and the risk of reporting an incorrect interval will increase
B)The resulting margin of error will decrease and the risk of reporting an incorrect interval will increase
C)The resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
D)The resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease