Deck 8: Interval Estimation

Question 1

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

Answer 1

False

Question 2

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.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

Excel does not have a special function that allows to calculate t values.

Question 6

The t_df 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_df distribution is similar to the z distribution.

Question 7

To construct a 95% confidence interval for µ,the sampling distribution of must be _______.

Question 8

The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

Question 9

The ________ coefficient is equal to 1- α .

Question 10

The ___________ determine the extent of the broadness of the tails of the distribution.

Question 11

The t distribution table lists t<sub>df values for selected lower-tail probabilities and degrees of freedom df.

FALSE</sub>

Question 12

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 13

The t_df distribution has broader tails than the z distribution.

Question 14

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 15

The sampling distribution of is based on a normal distribution on samples of any size.

Question 16

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

Question 17

The width of the confidence interval is _____ times the margin of error.

Question 18

It is important to know that __________ is increased when we estimate the population standard deviation with the sample standard deviation.

Question 19

If a small segment of the population is sampled then an estimate will be less precise.

Question 20

A confidence interval is generally associated with a(n)_____________.

Question 21

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 22

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.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 23

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.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 24

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 25

At an 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 26

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 27

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

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

Question 28

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 29

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) 120 ± 1.645(550/5)
B) 120 ± 1.96(550/5)
C) 550 ± 1.645(120/5)
D) 550 ± 1.96(120/5)

Question 30

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) A
B) B
C) C
D) D

Question 31

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

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

Question 32

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 33

If calculated required sample size is a noninteger value,we should always _______ calculated value.

Question 34

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 35

We draw a random sample of size 36 from a population with 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 36

We draw a random sample of size 25 from the normal population with 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 37

The parameter p represents the ________ of successes in the population.

Question 38

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

Question 39

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) None of the above

Question 40

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 41

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 its 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 42

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.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 43

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 44

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 45

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 46

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 with a standard deviation of $16 thousand.Assume the distribution is normally distributed.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 47

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 48

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.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

How do the t_df and z distributions differ?

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

Question 50

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 51

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 with a standard deviation of $16 thousand.Assume the distribution is normally distributed.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 52

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 53

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 54

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 55

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 56

The t_df 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) as the degrees of freedom go to infinity,the t distribution converges to the z distribution and both have asymptotic tails-that is,their tails become closer and closer to the horizontal axis but never touch it
D) Neither as the degrees of freedom go to infinity,the t distribution converges to the z distribution nor both have asymptotic tails-that is,their tails become closer and closer to the horizontal axis but never touch it

Question 57

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) [2.5261,2.8961]
C) [2.5615,2.8585]
D) [2.6358,2.7842]

Question 58

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 59

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 60

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 61

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 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 62

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 63

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 64

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 65

A sample of 1,400 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.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 66

A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy".Construct a 99% confidence interval of the proportion of American adults who viewed 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 67

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 68

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 69

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

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

Question 70

A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy".Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."

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

Question 71

A sample of 1,400 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.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 72

According to a report in USAToday (February 1,2012),more and more parents are helping their young adult children get homes.Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received 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 received help from their parents.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 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 liter when constructing a 99% confidence interval?

A) 831.39
B) 832
C) 832.39
D) 833

Question 74

A medical devices company wants to know the number of hours its 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 hour when calculating a 98% confidence interval?

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

Question 75

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 76

According to a report in USAToday (February 1,2012),more and more parents are helping their young adult children buy homes.You would like to construct a 90% confidence interval of the proportion of all young adults in Louisville,Kentucky,who received help from their parents in buying a home.How large a sample should you take so that the margin of error is no more than 0.06?

A) n = 114
B) n = 188
C) n = 267
D) Cannot be determined.

Question 77

According to a report in USAToday (February 1,2012),more and more parents are helping their young adult children get homes.Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received 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 received help from their parents.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

Question 78

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

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

Question 79

The minimum sample size n required to estimate a population mean with 95% confidence and the assumed estimate of the population standard deviation 6.5 was found to be 124.Which of the following is the approximate value of the assumed desired margin of error?

A) D = 0.9220
B) D = 0.9602
C) D = 1.1441
D) D = 1.3090

Question 80

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