Question 1

When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of $\hat { p }$
= )4,the interval is based on:

Accepted Answer

A) The z distribution. 
B) The t distribution. 
C) The exponential distribution. 
D) The Poisson distribution. 
E) None of thesE. 
A) The z distribution. 
B) The t distribution. 
C) The exponential distribution. 
D) The Poisson distribution. 
E) None of thesE. A

Question 2

When the population is normally distributed and the population standard deviation ? is unknown,then for any sample size n,the sampling distribution of $\bar { X }$ 
is based on the z distribution.

Accepted Answer

A) True 
 B)False  False

Question 3

An insurance analyst working for a car insurance company would like to determine the proportion of accident claims covered by the company.A random sample of 240 claims shows that the insurance company covered 90 accident claims,while 150 claims were not covered.Use a confidence interval of 95 percent and determine the margin of error.

Accepted Answer

A) .01513 
B) .03125 
C) .06125 
D) .02965 
A) .01513 
B) .03125 
C) .06125 
D) .02965 C

Question 4

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.

Accepted Answer

A)  $\left[ \begin{array} { l l } 
48.36 & 50.24
\end{array} \right]$ 
B)  $[ 43.27 \quad 55.33 ]$ 
C)  $\left[ \begin{array} { l l } 
47.29 & 51.31
\end{array} \right]$ 
D)  $[ 47.88$$ \quad$$ \quad$$50.72 ]$ 
E)  $[ 46.47 \quad 52.13 ]$ 
A)  $\left[ \begin{array} { l l } 
48.36 & 50.24
\end{array} \right]$ 
B)  $[ 43.27 \quad 55.33 ]$ 
C)  $\left[ \begin{array} { l l } 
47.29 & 51.31
\end{array} \right]$ 
D)  $[ 47.88$$ \quad$$ \quad$$50.72 ]$ 
E)  $[ 46.47 \quad 52.13 ]$

Question 5

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

Accepted Answer

A) Stays the same 
B) Decreases 
C) Increases 
A) Stays the same 
B) Decreases 
C) Increases

Question 6

The 95 percent confidence interval for the average weight of a product is from 72.23 lbs.to 77.77 lbs.Can we conclude that μ = 77,using a 95 percent confidence interval? Explain your answer.

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

A sample of 2,000 people yielded $\widehat { p }$
= )52.Calculate a 95 percent confidence interval for p.

Accepted Answer

A)  $\left[ \begin{array} { l l } 
.509 & .531
\end{array} \right]$ 
B)  $[ .494 \quad .546 ]$ 
C)  $\left[ \begin{array} { l l } 
498 & .542
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 
.502 & .538
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 
.509 & .531
\end{array} \right]$ 
B)  $[ .494 \quad .546 ]$ 
C)  $\left[ \begin{array} { l l } 
498 & .542
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 
.502 & .538
\end{array} \right]$

Question 8

The success rate of a procedure is 37 per 120 cases in a sample.Find a 95 percent confidence interval for the actual success proportion of the procedure.

Accepted Answer

A)  $\left[ \begin{array} { l l } 
.2975 & .4425
\end{array} \right]$ 
B)  $[ .2389 \quad .3776 ]$ 
C)  $\left[ \begin{array} { l l } 
.2836 & .4564
\end{array} \right]$ 
D)  $[ .2250 \quad .3910 ]$ 
A)  $\left[ \begin{array} { l l } 
.2975 & .4425
\end{array} \right]$ 
B)  $[ .2389 \quad .3776 ]$ 
C)  $\left[ \begin{array} { l l } 
.2836 & .4564
\end{array} \right]$ 
D)  $[ .2250 \quad .3910 ]$

Question 9

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 statistics to use is ________.

Accepted Answer

A) t 
B) z 
C) χ 
D) p 
A) t 
B) z 
C) χ 
D) p

Question 10

A computer manufacturing company has sent a mail survey to 2800 of its randomly selected customers that have purchased a new personal computer.The survey asked the customers whether or not they were satisfied with the computer.800 customers responded to the survey.640 customers indicated that they were satisfied,while 160 customers indicated they were not satisfied with their new computer.Construct a 96 percent confidence interval estimate of the true proportion of customers satisfied with their new computer.

Accepted Answer

A)  $[ .771 \quad .829 ]$ 
B)  $[ .788 \quad .812 ]$ 
C)  $[ .775 \quad .825 ]$ 
D)  $\left[ \begin{array} { l l } 
.785 & .816
\end{array} \right]$ 
A)  $[ .771 \quad .829 ]$ 
B)  $[ .788 \quad .812 ]$ 
C)  $[ .775 \quad .825 ]$ 
D)  $\left[ \begin{array} { l l } 
.785 & .816
\end{array} \right]$

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

A) Standard deviation of the sample 
B) Sample size n 
C) Number of degrees of freedom 
D) z distribution 
A) Standard deviation of the sample 
B) Sample size n 
C) Number of degrees of freedom 
D) z distribution

Question 14

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

Accepted Answer

A) Always 
B) Sometimes 
C) Never 
A) Always 
B) Sometimes 
C) Never

Question 15

In 1995,13,000 WWW users were surveyed and asked about their willingness to pay fees for access to websites.Of these,2,938 were definitely not willing to pay such fees.Construct a 95 percent confidence interval for the proportion definitely unwilling to pay fees.

Accepted Answer

A)  $\left[ \begin{array} { l l } 
0.286 & 0.302
\end{array} \right]$ 
B)  $[ 0.219 \quad 0.233 ]$ 
C)  $[ 0.220 \quad 0.232 ]$ 
D)  $\left[ \begin{array} { l l } 
0.212 & 0.241
\end{array} \right]$ 
E)  $[ 0.214 \quad 0.245 ]$ 
A)  $\left[ \begin{array} { l l } 
0.286 & 0.302
\end{array} \right]$ 
B)  $[ 0.219 \quad 0.233 ]$ 
C)  $[ 0.220 \quad 0.232 ]$ 
D)  $\left[ \begin{array} { l l } 
0.212 & 0.241
\end{array} \right]$ 
E)  $[ 0.214 \quad 0.245 ]$

Question 16

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.

Accepted Answer

A) True 
 B)False

Question 17

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.

Accepted Answer

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

Question 18

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

Accepted Answer

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. 
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 19

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

Accepted Answer

A) Stays the same 
B) Decreases 
C) Increases 
A) Stays the same 
B) Decreases 
C) Increases

Question 20

A sample of 2,000 people yielded $\hat { p }$
= )52.What is the variance of the population proportion?

Accepted Answer

A) .0056 
B) .0112 
C) .00012 
D) .0161 
A) .0056 
B) .0112 
C) .00012 
D) .0161

When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of $\hat { p }$ = )4,the interval is based on:

When the population is normally distributed and the population standard deviation ? is unknown,then for any sample size n,the sampling distribution of $\bar { X }$ is based on the z distribution.

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

The 95 percent confidence interval for the average weight of a product is from 72.23 lbs.to 77.77 lbs.Can we conclude that μ = 77,using a 95 percent confidence interval? Explain your answer.

A sample of 2,000 people yielded $\widehat { p }$ = )52.Calculate a 95 percent confidence interval for p.

The success rate of a procedure is 37 per 120 cases in a sample.Find a 95 percent confidence interval for the actual success proportion of the procedure.

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 statistics to use is ________.

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

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

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

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

In 1995,13,000 WWW users were surveyed and asked about their willingness to pay fees for access to websites.Of these,2,938 were definitely not willing to pay such fees.Construct a 95 percent confidence interval for the proportion definitely unwilling to pay fees.

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.

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.

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

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

A sample of 2,000 people yielded $\hat { p }$ = )52.What is the variance of the population proportion?

An Introduction to Business Statistics

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics: Numerical Methods

Probability

Discrete Random Variables

Continuous Random Variables

Sampling and Sampling Distributions

Hypothesis Testing

Comparing Two Means and Two Proportions

Filters

Exam 8: Confidence Intervals

When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of p^\hat { p }p^​ = )4,the interval is based on:

When the population is normally distributed and the population standard deviation ? is unknown,then for any sample size n,the sampling distribution of Xˉ\bar { X }Xˉ is based on the z distribution.

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

The 95 percent confidence interval for the average weight of a product is from 72.23 lbs.to 77.77 lbs.Can we conclude that μ = 77,using a 95 percent confidence interval? Explain your answer.

A sample of 2,000 people yielded p^\widehat { p }p​ = )52.Calculate a 95 percent confidence interval for p.

The success rate of a procedure is 37 per 120 cases in a sample.Find a 95 percent confidence interval for the actual success proportion of the procedure.

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 statistics to use is ________.

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

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

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

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

In 1995,13,000 WWW users were surveyed and asked about their willingness to pay fees for access to websites.Of these,2,938 were definitely not willing to pay such fees.Construct a 95 percent confidence interval for the proportion definitely unwilling to pay fees.

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.

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.

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

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

A sample of 2,000 people yielded p^\hat { p }p^​ = )52.What is the variance of the population proportion?

An Introduction to Business Statistics

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics: Numerical Methods

Probability

Discrete Random Variables

Continuous Random Variables

Sampling and Sampling Distributions

Hypothesis Testing

Comparing Two Means and Two Proportions

Filters

When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of $\hat { p }$ = )4,the interval is based on:

When the population is normally distributed and the population standard deviation ? is unknown,then for any sample size n,the sampling distribution of $\bar { X }$ is based on the z distribution.

A sample of 2,000 people yielded $\widehat { p }$ = )52.Calculate a 95 percent confidence interval for p.

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

A sample of 2,000 people yielded $\hat { p }$ = )52.What is the variance of the population proportion?