Deck 8: Confidence Intervals

Question 1

When the level of confidence and sample standard deviation remain the same,a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50.

Answer 1

True

Question 2

The more variable that the population measurements are,the larger the sample size that is needed to accurately estimate µ at a specific confidence level.

Answer 2

True

Question 3

First,a 90 percent confidence interval is constructed from a sample size of 100.Then,for the same identical data,a 92 percent confidence interval is constructed.The width of the 90 percent interval is wider than the 92 percent confidence interval.

Answer 3

False

Question 4

If σ is unknown and there is no preliminary sample available to estimate σ,the range can be utilized to determine an estimate of σ when finding sample size.

Question 5

When the level of confidence and the sample size remain the same,a confidence interval for a population mean μ will be wider when the sample standard deviation s is small than when s is large.

Question 6

When the level of confidence and sample size remain the same,a confidence interval for a population proportion,p,will be narrower when
is larger than when 11ec8fec_68f9_6078_bdf7_8f90d9ecdd59_TB2569_11
is smaller.

Question 7

The t distribution always has n degrees of freedom.

Question 8

When constructing a confidence interval for a sample proportion,the t distribution is appropriate if the sample size is small.

Question 9

Assuming the same level of significance α,as the sample size increases,the value of t_α/2 approaches the value of z_α/2.

Question 10

When determining the sample size (n)for a confidence interval for ρ,if you have no idea what value p is (it could be any value between 0 and 1),use p = .5.

Question 11

When determining the sample size n,if the value found for n is 79.2,we would choose to sample 79 observations.

Question 12

When determining the sample size (n)for a confidence interval for ρ,if past experience tells us that p is at least 0.8,use p = .2.

Question 13

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion p,having a given error bound E,we choose a value of
that makes
as small as reasonably possible.

Question 14

The quantity √[(N − n)/N] in the confidence intervals for μ and τ is called the finite population correction and is always less than 1.

Question 15

When determining the sample size (n)for a confidence interval for ρ,if you are using a previous sample,use the reasonable value of ρ that is closest to 0.25.

Question 16

When the level of confidence and sample proportion
remain the same,a confidence interval for a population proportion,p,based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400.

Question 17

When the sample size and sample standard deviation remain the same,a 99 percent confidence interval for a population mean,μ,will be narrower than the 95 percent confidence interval for μ.

Question 18

When the population is normally distributed and the population standard deviation σ is unknown,then for any sample size n,the sampling distribution of
is based on the z distribution.

Question 19

The standard error of the sample mean is s/√n.

Question 20

When the margin of error is added to and subtracted from the sample mean,an interval is formed that will contain μ with a probability of (1 − α).

Question 21

The exact spread of the t distribution depends on the _________.

A) standard deviation of the sample
B) sample size n
C) number of degrees of freedom
D) z distribution

Question 22

As standard deviation increases,sample size _____________ to achieve a specified level of confidence.

A) increases
B) decreases
C) remains the same

Question 23

When constructing a confidence interval for a population mean,if a population is normally distributed and a small sample is taken,then the distribution of is based on the ____________ distribution.

A) z
B) t
C) neither the z nor the t distribution
D) both the z and the t distribution

Question 24

When the population is normally distributed,population standard deviation σ is unknown,and the sample size is n = 15,the confidence interval for the population mean μ is based on

A) the z (normal)distribution.
B) the t distribution.
C) the binomial distribution.
D) the Poisson distribution.
E) None of the other choices is correct.

Question 25

When the sample size and the sample proportion remain the same,a 90 percent confidence interval for a population proportion p will be ______________ the 99 percent confidence interval for p.

A) wider than
B) narrower than
C) equal to

Question 26

A confidence interval for the population mean is meant to contain a specified percentage of the individual population measurements.

Question 27

When determining the sample size,if the value found is not an integer initially,you should ____________ choose the next highest integer value.

A) always
B) sometimes
C) never

Question 28

The width of a confidence interval will be

A) narrower for 98 percent confidence than for 90 percent confidence.
B) wider for a sample size of 64 than for a sample size of 36.
C) wider for 99 percent confidence than for 95 percent confidence
D) narrower for a sample size of 25 than for a sample size of 36.
E) None of the other choices is correct.

Question 29

A tolerance interval is always longer than a corresponding confidence interval.

Question 30

A tolerance interval is meant to contain a specified percentage of the individual population measurements.

Question 31

Which of the following is an advantage of a confidence interval estimate over a point estimate for a population parameter?

A) Interval estimates are more precise than point estimates.
B) Interval estimates are less accurate than point estimates.
C) Interval estimates are both more accurate and more precise than point estimates.
D) Interval estimates take into account the fact that the statistic being used to estimate the population parameter is a random variable.

Question 32

The t distribution approaches the _______________ distribution as the sample size ___________.

A) binomial,increases
B) binomial,decreases
C) z,decreases
D) z,increases

Question 33

The width of a confidence interval will be

A) narrower for 99 percent confidence than for 95 percent confidence.
B) wider for a sample size of 100 than for a sample size of 50.
C) narrower for 90 percent confidence than for 95 percent confidence.
D) wider when the sample standard deviation (s)is small than when s is large.

Question 34

When the level of confidence and sample size remain the same,a confidence interval for a population proportion,p,will be ______________ when is larger than when 11ec8fec_dcc7_868b_bdf7_b7e05f5c77bd_TB2569_11
Is smaller.

A) wider
B) narrower
C) neither wider nor narrower (they will be the same)

Question 35

A confidence interval increases in width as

A) the level of confidence increases.
B) n decreases.
C) s increases.
D) All of the other choices are correct.

Question 36

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion p,having a given error bound E,we choose a value of that

A) makes
As small as reasonably possible.
B) makes 11ec8fed_10d0_e7fc_bdf7_791f7c814a39_TB2569_11
As large as reasonably possible.
C) makes 11ec8fed_10d0_e7fc_bdf7_791f7c814a39_TB2569_11
As close to .5 as reasonably possible.
D) makes 11ec8fed_10d0_e7fc_bdf7_791f7c814a39_TB2569_11
As close to .25 as reasonably possible.
E) makes 11ec8fed_10d0_e7fc_bdf7_791f7c814a39_TB2569_11

Question 37

When the level of confidence and sample proportion remain the same,a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.

A) wider than
B) narrower than
C) equal to

Question 38

When the level of confidence and sample standard deviation remain the same,a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.

A) wider than
B) narrower than
C) equal to

Question 39

When the sample size and sample standard deviation remain the same,a 99 percent confidence interval for a population mean,μ,will be _________________ the 95 percent confidence interval for μ.

A) wider than
B) narrower than
C) equal to

Question 40

When the level of confidence and the sample size remain the same,a confidence interval for a population mean μ will be ________________ when the sample standard deviation s is small than when s is large.

A) wider
B) narrower
C) neither wider nor narrower (they will be the same)

Question 41

In determining the sample size to estimate a population proportion,as p approaches .5,the calculated value of the sample size ______________.

A) stays the same
B) decreases
C) increases

Question 42

When establishing the confidence interval for the average weight of a cereal box,assume that the population standard deviation is known to be 2 ounces.Based on a sample,the average weight of a sample of 20 boxes is 16 ounces.The appropriate test statistic to use is ________.

A) t
B) z
C) χ
D) p

Question 43

As the margin of error decreases,the width of the confidence interval _______________.

A) stays the same
B) decreases
C) increases

Question 44

Assuming the same level of significance α,as the sample size increases,the value of t_α/2 ___________ approaches the value of z_α/2.

A) always
B) sometimes
C) never

Question 45

The tolerance interval of 95.44 percent is ________ a 95.44 percent confidence interval.

A) the same width as
B) narrower than
C) wider than

Question 46

A confidence interval for the population mean is an interval constructed around the ____________.

A) sample mean
B) population mean
C) z test statistic
D) t test statistic

Question 47

There is little difference between the values of t_α/2 and z_α/2 when

A) the sample size is small.
B) the sample size is large.
C) the sample mean is small.
D) the sample mean is large.
E) the sample standard deviation is small.

Question 48

As the significance level α increases,the width of the confidence interval _______________.

A) stays the same
B) decreases
C) increases

Question 49

A psychologist is collecting data on the time it takes to learn a certain task.For 50 randomly selected adult subjects,the sample mean is 16.40 minutes and the sample standard deviation is 4.00 minutes.Construct the 95 percent confidence interval for the mean time required by all adults to learn the task.

A) [8.56,24.24]
B) [15.47,17.33]
C) [16.24,16.56]
D) [15.26,17.54]
E) [17.12,48.48]

Question 50

When constructing a confidence interval,as the confidence level required in estimating the mean increases,the width of the confidence interval ______________.

A) stays the same
B) decreases
C) increases

Question 51

Researchers have studied the role that the age of workers has in determining the hours per month spent on personal tasks.A sample of 1,686 adults were observed for one month.The data follow. Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25- to 44-year-olds.

A) [3.96,4.12]
B) [3.97,4.11]
C) [3.98,4.10]
D) [2.16,5.92]
E) [3.95,4.13]

Question 52

The U.S.Department of Health and Human Services collected sample data for 772 males between the ages of 18 and 24.That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches.Find the 99 percent confidence interval for the mean height of all males between the ages of 18 and 24.

A) [63.19,76.21]
B) [62.49,76.91]
C) [69.65,69.75]
D) [69.47,69.93]
E) [69.44,69.96]

Question 53

If everything else is held constant,decreasing the margin of error causes the required sample size to ____________.

A) stay the same
B) decrease
C) increase

Question 54

Unoccupied seats on flights cause airlines to lose revenue.Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year.225 flight records are randomly selected and the number of unoccupied seats is noted,with a sample mean of 11.6 seats and a standard deviation of 4.1 seats.Calculate a 90 percent confidence interval for μ,the mean number of unoccupied seats per flight during the past year.

A) [4.86,18.34]
B) [11.25,11.95]
C) [11.57,11.63]
D) [11.15,12.05]
E) [11.30,12.20]

Question 55

A researcher for a paint company is measuring the level of a certain chemical contained in a particular type of paint.If the paint contains too much of this chemical,the quality of the paint will be compromised.On average,each can of paint contains 10 percent of the chemical.How many cans of paint should the sample contain if the researcher wants to be 98 percent certain of being within 1 percent of the true proportion of this chemical?

A) 4870
B) 1107
C) 26
D) 645

Question 56

As the stated confidence level decreases,the width of the confidence interval _______________.

A) stays the same
B) decreases
C) increases

Question 57

As the sample size n increases,the width of the confidence interval _______________.

A) stays the same
B) decreases
C) increases

Question 58

When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of = .4,the interval is based on

A) the z distribution.
B) the t distribution.
C) the exponential distribution.
D) the Poisson distribution.
E) None of the other choices is correct.

Question 59

As the standard deviation (σ)decreases,the width of the confidence interval _______________.

A) stays the same
B) decreases
C) increases

Question 60

In a study of factors affecting whether soldiers decide to reenlist,320 subjects were measured for an index of satisfaction.The sample mean is 28.8 and the sample standard deviation is 7.3.Use the given sample data to construct the 98 percent confidence interval for the population mean for level of satisfaction.

A) [27.85,29.75]
B) [27.96,29.64]
C) [11.82,45.78]
D) [28.75,28.85]
E) [28.60,29.00]

Question 61

On a standard IQ test,the standard deviation is 15.How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5)and we want 97 percent confidence in the results?

A) 4,239
B) 283
C) 212
D) 131
E) 66

Question 62

An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas.They test a sample of five cars and obtain a mean of 28.2 miles.Assuming that the standard deviation is 2.7 miles,find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.

A) [26.16,30.24]
B) [20.70,35.70]
C) [24.85,31.55]
D) [26.70,29.70]
E) [25.83,30.57]

Question 63

Unoccupied seats on flights cause airlines to lose revenue.Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year.225 flight records are randomly selected and the number of unoccupied seats is noted,with a sample mean of 11.6 seats and a standard deviation of 4.1 seats.How many flights should we select if we wish to estimate μ to within 2 seats and be 95 percent confident?

A) 130
B) 65
C) 33
D) 17
E) 12

Question 64

An experiment was conducted to determine the effectiveness of a method designed to remove oil wastes found in soil.Three contaminated soil samples were treated.After 95 days,the percentage of contamination removed from each soil sample was measured,with a mean of 49.3 percent and a standard deviation of 1.5 percent.If we wished to narrow the boundary around μ for a 98 percent confidence interval to within 0.5 percent,how many soil samples should be in our experiment.

A) 437
B) 33
C) 9
D) 6
E) 3

Question 65

A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years.A random sample of 20 defaulted loans yielded a mean of $67,918 with a standard deviation of $16,552.40.Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years.

A) [66,487,69,349]
B) [39,299,96,537]
C) [57,329,78,507]
D) [61,829,74,007]
E) [61,519,74,317]

Question 66

There is an average of 22.455 employees at 22 office furniture dealers in a major metropolitan area,with a standard deviation of 18.52.Construct a 99 percent confidence interval for the true mean number of full-time employees at office furniture dealers.

A) [11.014,33.896]
B) [11.275,33.635]
C) [12.284,32.626]
D) [12.513,32.397]
E) [20.072,24.838]

Question 67

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup.Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces.Construct a 99 percent confidence interval for the true machine-fill amount.

A) [5.75,5.99]
B) [5.85,6.05]
C) [5.90,6.00]
D) [5.70,6.16]
E) [5.80,6.06]

Question 68

A botanist measures the heights of 16 seedlings and obtains a mean and standard deviation of 72.5 cm and 4.5 cm,respectively.Find the 95 percent confidence interval for the mean height of seedlings in the population from which the sample was selected.

A) [62.91,82.09]
B) [70.30,74.70]
C) [70.10,74.90]
D) [70.54,74.46]
E) [71.90,73.10]

Question 69

A local company makes a candy that is supposed to weigh 1.00 ounces.A random sample of 25 pieces of candy produces a mean of 0.996 ounces with a standard deviation of 0.004 ounces.Construct a 98 percent confidence interval for the mean weight of all such candy.

A) [0.9645,1.0275]
B) [0.9956,0.9964]
C) [0.9860,1.0060]
D) [0.9940,0.9980]
E) [0.9942,0.9978]

Question 70

Recently,a case of food poisoning was traced to a particular restaurant chain.The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur.Despite the response from the restaurant chain,many consumers refused to visit the restaurant for some time after the event.A survey was conducted three months after the food poisoning occurred,with a sample of 319 former customers contacted.Of the 319 contacted,29 indicated that they would not go back to the restaurant because of the potential for food poisoning.Construct a 95 percent confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain three months after the event.

A) [.059,.122]
B) [.090,.091]
C) [.000,.196]
D) [.240,.339]
E) [.118,.244]

Question 71

A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds (σ = 0.1).When the machine is properly calibrated,the mean inflation pressure is 13.5 pounds,but uncontrollable factors can cause the pressure of individual footballs to vary.For quality control purposes,the manufacturer wishes to estimate the mean inflation pressure to within 0.025 pounds of its true value with 99 percent confidence.What sample size should be used?

A) 677
B) 107
C) 35
D) 27
E) 11

Question 72

A sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects.Their mean score is 71.2 with a standard deviation of 10.5.Construct the 99 percent confidence interval for the mean score of all subjects.

A) [40.26,102.14]
B) [63.46,78.94]
C) [60.66,81.74]
D) [64.44,77.96]
E) [63.21,79.19]

Question 73

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS)of their patients.In 2003,the average LOS for non-heart patients was 4.6 days.A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2008 of 3.8 days and a standard deviation of 1.2 days.How large a sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean?

A) 3
B) 7
C) 32
D) 48
E) 96

Question 74

An experiment was conducted to determine the effectiveness of a method designed to remove oil wastes found in soil.Three contaminated soil samples were treated.After 95 days,the percentage of contamination removed from each soil sample was measured,with a mean of 49.3 percent and a standard deviation of 1.5 percent.Estimate the mean percentage of contamination removed at a 98 percent confidence level.

A) [48.36,50.24]
B) [43.27,55.33]
C) [47.29,51.31]
D) [47.88,50.72]
E) [46.47,52.13]

Question 75

In a random sample of 651 computer scientists who subscribed to a web-based daily news update,it was found that the average salary was $46,816 with a population standard deviation of $12,557.Calculate a 91 percent confidence interval for the mean salary of computer scientists.

A) [$25,469,$68,163]
B) [$46,592,$47,040]
C) [$46,157,$47,475]
D) [$46,783,$46,849]
E) [$45,981,$47,650]

Question 76

A local company makes a candy that is supposed to weigh 1.00 ounces.A random sample of 25 pieces of candy produces a mean of 0.996 ounces with a standard deviation of 0.004 ounces.How many pieces of candy must we sample if we want to be 99 percent confident that the sample mean is within 0.001 ounces of the true mean?

A) 126
B) 124
C) 107
D) 12
E) 6

Question 77

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS)of their patients.In 2003,the average LOS for non-heart patients was 4.6 days.A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2008 of 3.8 days and a standard deviation of 1.2 days.Calculate a 95 percent confidence interval for the population mean LOS for non-heart patients in these hospitals in 2008.

A) [3.24,4.36]
B) [3.67,3.93]
C) [3.34,4.26]
D) [3.38,4.22]
E) [3.27,4.33]

Question 78

At the end of 1990,1991,and 1992,the average prices of a share of stock in a portfolio were $34.83,$34.65,and $31.26 respectively.To investigate the average share price at the end of 1993,a random sample of 30 stocks was drawn and their closing prices on the last trading day of 1993 were observed with a mean of 33.583 and a standard deviation of 19.149.Estimate the average price of a share of stock in the portfolio at the end of 1993 with a 90 percent confidence interval.

A) [27.646,39.523]
B) [26.732,40.434]
C) [32.514,34.651]
D) [32.533,34.633]
E) [32.269,34.897]

Question 79

An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas.They test a sample of five cars and obtain a mean of 28.2 miles.How many cars should the environmental group test if they wish to estimate μ,mean miles per 1 gallon,to within 0.5 miles and be 99 percent confident? Assume a population standard deviation of 2.7 miles.

A) 25
B) 124
C) 194
D) 618
E) 619

Question 80

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup.Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces.How large a sample of soups would we need to be 95 percent confident that the sample mean is within 0.03 ounces of the population mean?

A) 97
B) 96
C) 73
D) 62
E) 10