Question 1

One way of reducing the width of a confidence interval is to reduce the size of the sample taken.

Accepted Answer

A) True 
 B)False

Question 2

When is the finite population correction factor used?

Accepted Answer

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

Question 3

$$\text { For } n = 800 \text { and } \hat { p } = .99 \text {, is the sample size large enough to construct a confidence for } p \text { ? }$$

Accepted Answer

The answer of \[\text { For } n = 800...

Question 4

It is desired to estimate the proportion of college students who feel a sudden relief now that their statistics class is over. How many students must be sampled in order to estimate the true proportion to within 2% at the 90% confidence level?

Accepted Answer

A)  $n = 189$ 
B)  $n = 2401$ 
C)  $n = 133$ 
D)  $n = 1692$ 
E)  Cannot determine because no estimate of $p$ or $q$ exists in this problem

Question 5

Calculate the percentage of the population sampled if n = 100 and N = 10,000. 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 6

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature Construct an approximate 95% confidence interval for the true proportion of all voters in the state who favor approval.

Accepted Answer

A)  $0.47 \pm 0.049$ 
B)  $0.47 \pm 0.034$ 
C)  $0.47 \pm 0.017$ 
D)  $0.47 \pm 0.025$

Question 7

One way of reducing the width of a confidence interval is to reduce the confidence level.

Accepted Answer

A) True 
 B)False

Question 8

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). The researcher claimed that the average GPA of all male students exceeded 2.94. Using the confidence interval supplied above,
How do you respond to this claim?

Accepted Answer

A)  We are 95% confident that the researcher is correct. 
B)  We are 95% confident that the researcher is incorrect. 
C)  We are 100% confident that the researcher is incorrect. 
D)  We cannot make any statement regarding the average GPA of male university students at the 95% confidence level.

Question 9

Suppose you selected a random sample of n = 7 measurements from a normal distribution. 
Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

Accepted Answer

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

Question 10

How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided asample mean and standard deviation of $14.00 and $2.50, respectively. Use this information to construct a 90% confidence interval for the mean.

Accepted Answer

A)  $14 \pm 1.833 ( 2.50 / \sqrt { 10 } )$ 
B)  $14 \pm 1.383 ( 2.50 / \sqrt { 10 } )$ 
C)  $14 \pm 1.796 ( 2.50 / \sqrt { 10 } )$ 
D)  $14 \pm 1.812 ( 2.50 / \sqrt { 10 } )$

Question 11

Find the value of t0 such that the following statement is true: P(-t0 ≤t ≤t0) = .99 where df = 9.

Accepted Answer

A)  1.833 
B)  2.2821 
C)  2.262 
D)  3.250

Question 12

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 13

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles.

SAMPLE PROPORTION $= .396226$
SAMPLE SIZE $= 159$

$\mathrm { UPPER } \mathrm { LIMIT } = .46492$
LOWER LIMIT $= .331153$

Is the sample large enough for the interval to be valid?

Accepted Answer

A)  No, the sample size should be at 10% of the population. 
B)  Yes, since n^p and n^q are both greater than 15. 
C)  No, the population of college students is not normally distributed. 
D)  Yes, since n > 30.

Question 14

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 99% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). Explain what the phrase "99% confident" means.

Accepted Answer

A)  99% of the similarly constructed intervals would contain the value of the sample mean. 
B)  In repeated sampling, 99% of the intervals constructed would contain µ. 
C)  99% of the population values will fall within the interval. 
D)  99% of the sample means from similar samples fall within the interval.

Question 15

How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled results show that the sample mean and sample standard deviation were $70.00 and $17.50, respectively. Use this information to create a 95 percent confidence interval for the population mean.

Accepted Answer

A)  $70 \pm 2.262 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$ 
B)  $70 \pm 1.960 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$ 
C)  $70 \pm 2.228 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$ 
D)  $70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

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

One way of reducing the width of a confidence interval is to reduce the size of the sample taken.

When is the finite population correction factor used?

$\text { For } n = 800 \text { and } \hat { p } = .99 \text {, is the sample size large enough to construct a confidence for } p \text { ? }$

It is desired to estimate the proportion of college students who feel a sudden relief now that their statistics class is over. How many students must be sampled in order to estimate the true proportion to within 2% at the 90% confidence level?

Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain.

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature Construct an approximate 95% confidence interval for the true proportion of all voters in the state who favor approval.

One way of reducing the width of a confidence interval is to reduce the confidence level.

Suppose you selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

Find the value of t0 such that the following statement is true: P(-t0 ≤t ≤t0) = .99 where df = 9.

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 99% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180) . Explain what the phrase "99% confident" means.