Question 1

Calculate the percentage of the population sampled if n = 250 and N = 1000. Should the  standard error in this situation be multiplied by a finite population correction factor?
Explain.

Accepted Answer

The answer of Calculate the percentage of the population sampled...

Question 2

Suppose you selected a random sample of $n = 29$ measurements from a normal distribution. Compare the standard normal z value with the corresponding $t$ value for a $95 \%$ confidence interval.

Accepted Answer

The answer of Suppose you selected a random sample of...

Question 3

For $n = 40 \text { and } \hat { p } = .35 \text {, is }$ s the sample size large enough to construct a confidence for p?

Accepted Answer

The answer of For \(n = 40 \text { and...

Question 4

A newspaper reports on the topics that teenagers most want to discuss with their parents. the findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 90% confidence level.

Accepted Answer

The answer of A newspaper reports on the topics that...

Question 5

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $= 3.1$.
a. Find a $90 \%$ confidence interval for the population mean $\mu$.
b. Find a $95 \%$ confidence interval for $\mu$.
c. Find a $99 \%$ confidence interval for $\mu$.
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

Accepted Answer

The answer of A random sample of 80 observations produced...

Question 6

A random sample of 50 employees of a large company was asked the question, "Do you  participate in the company's stock purchase plan?" The answers are shown below.

$$\begin{array} { l l l l l l l l l l } 
\text { yes } & \text { no } & \text { no } & \text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } & \text { no } & \text { no } \
\text { no } & \text { yes } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } \
\text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { yes } \
\text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { no } & \text { yes } \
\text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes }
\end{array}$$ Use a 90% confidence interval to estimate the proportion of employees who participate in the company's stock purchase plan.

Accepted Answer

The answer of A random sample of 50 employees of...

Question 7

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean nicotine content of $26.2$ milligrams and standard deviation of $2.9$ milligrams for a sample of $n = 95$ cigarettes. Find a $95 \%$ confidence interval for $\mu$.

Accepted Answer

The answer of To help consumers assess the risks they...

Question 8

A random sample of $n = 100$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$. Calculate a $95 \%$ confidence interval if $\bar { x } = 26$ and $s ^ { 2 } = 16$.

Accepted Answer

The answer of A random sample of $n = 100$...

Question 9

The following sample of 16 measurements was selected from a population that is  approximately normally distributed.

$\begin{array} { l l l l l l l l } 61 & 85 & 92 & 77 & 83 & 81 & 75 & 78 \end{array}$
$\begin{array} { l l l l l l l l } 95 & 87 & 69 & 74 & 76 & 84 & 80 & 83 \end{array}$

Construct a 90% confidence interval for the population mean.

Accepted Answer

The answer of The following sample of 16 measurements was...

Question 10

A marketing research company is estimating the average total compensation of CEOs in  the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

Accepted Answer

The answer of A marketing research company is estimating the...

Question 11

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood.

$\begin{array}{rl}
X=&\text { saleprice }\
\
\text {SAMPLE MEAN OF X} =&46300 \
\text {SAMPLE STANDARD DEV } =&13747 \ \text {SAMPLE SIZE OF X} =&25 \
\text {CONEIDENCE}=& 90 \
\
\text { UPPER LIMIT }= & 51003.90 \
\text { SAMPLE MEAN OF X }= & 46300 \
\text { LOWER LIMIT }= & 41596.10
\end{array}$

A friend suggests that the mean sale price of homes in this neighborhood is $47,000. Comment on your friend's suggestion.

Accepted Answer

The answer of A computer package was used to generate...

Question 12

A marketing research company is estimating the average total compensation of CEOs in  the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000?

Accepted Answer

The answer of A marketing research company is estimating the...

Question 13

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus.
Which of the following would represent the target parameter of interest?

A) $\mu$
B) $p$

Accepted Answer

The target parameter of interest is the average parking time, which is represented by the population mean, denoted by $\mu$.

Question 14

Suppose that 100 samples of size $n = 50$ are independently chosen from the same population and that each sample is used to construct its own $95 \%$ confidence interval for an unknown population mean $\mu$. How many of the 100 confidence intervals would you expect to actually contain $\mu$ ?

Accepted Answer

The answer of Suppose that 100 samples of size \(n...

Question 15

What is the rule of thumb for the finite population correction factor?

Accepted Answer

The answer of What is the rule of thumb for...

Question 16

Suppose you wanted to estimate a binomial proportion, p, correct to within .03 with probability 0.90. What size sample would need to be selected if p is known to be approximately 0.7?

Accepted Answer

The answer of Suppose you wanted to estimate a binomial...

Question 17

The following data represent the scores of a sample of 50 randomly chosen students on a standardized test.

$$\begin{array} { l l l l l l l l l l } 
39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \
71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \
79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \
85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \
90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99
\end{array}$$ a. Write a 95% confidence interval for the mean score of all students who took the test.
b. Identify the target parameter and the point estimator.

Accepted Answer

The answer of The following data represent the scores of...

Question 18

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$. Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$.49

Accepted Answer

The answer of A random sample of $n = 144$...

Question 19

A local men's clothing store is being sold. The buyers are trying to estimate the percentage  of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is within 3%?

Accepted Answer

The answer of A local men's clothing store is being...

Question 20

When is the finite population correction factor used?

Accepted Answer

The answer of When is the finite population correction factor...

Quiz 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

Calculate the percentage of the population sampled if n = 250 and N = 1000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain.

Suppose you selected a random sample of $n = 29$ measurements from a normal distribution. Compare the standard normal z value with the corresponding $t$ value for a $95 \%$ confidence interval.

For $n = 40 \text { and } \hat { p } = .35 \text {, is }$ s the sample size large enough to construct a confidence for p?

A random sample of $n = 100$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $95 \%$ confidence interval if $\bar { x } = 26$ and $s ^ { 2 } = 16$ .

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

Suppose that 100 samples of size $n = 50$ are independently chosen from the same population and that each sample is used to construct its own $95 \%$ confidence interval for an unknown population mean $\mu$ . How many of the 100 confidence intervals would you expect to actually contain $\mu$ ?

What is the rule of thumb for the finite population correction factor?

Suppose you wanted to estimate a binomial proportion, p, correct to within .03 with probability 0.90. What size sample would need to be selected if p is known to be approximately 0.7?

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ .49

When is the finite population correction factor used?

Quiz 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

Calculate the percentage of the population sampled if n = 250 and N = 1000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain.

Suppose you selected a random sample of n=29n = 29n=29 measurements from a normal distribution. Compare the standard normal z value with the corresponding ttt value for a 95%95 \%95% confidence interval.

For n=40 and p^=.35, is n = 40 \text { and } \hat { p } = .35 \text {, is }n=40 and p^​=.35, is s the sample size large enough to construct a confidence for p?

A random sample of n=100n = 100n=100 measurements was selected from a population with unknown mean μ\muμ and standard deviation σ\sigmaσ . Calculate a 95%95 \%95% confidence interval if xˉ=26\bar { x } = 26xˉ=26 and s2=16s ^ { 2 } = 16s2=16 .

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

What is the rule of thumb for the finite population correction factor?

Suppose you wanted to estimate a binomial proportion, p, correct to within .03 with probability 0.90. What size sample would need to be selected if p is known to be approximately 0.7?

A random sample of n=144n = 144n=144 measurements was selected from a population with unknown mean μ\muμ and standard deviation σ\sigmaσ . Calculate a 90%90 \%90% confidence interval if xˉ=3.55\bar { x } = 3.55xˉ=3.55 and s=s =s= .49

When is the finite population correction factor used?

Suppose you selected a random sample of $n = 29$ measurements from a normal distribution. Compare the standard normal z value with the corresponding $t$ value for a $95 \%$ confidence interval.

For $n = 40 \text { and } \hat { p } = .35 \text {, is }$ s the sample size large enough to construct a confidence for p?

A random sample of $n = 100$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $95 \%$ confidence interval if $\bar { x } = 26$ and $s ^ { 2 } = 16$ .

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ .49