question 1

The waiting times(in minutes) of a random sample of 21 people at a bank have a sample standard deviation of 3.2 minutes. Construct a confidence interval for the population variance 2 and the population standard deviation . Use a 95% level of confidence. Assume the sample is from a normally distributed population.

What is the confidence interval for the population variance 2?

(Round to one decimal place asneeded.)

Interpret the results. Select the correct choice below and fill in the answerbox(es) to complete your choice.

(Round to one decimal place asneeded.)

A.

With 5% confidence, you can say that the population variance is between ____ and ____

B.

With 5% confidence, you can say that the population variance is greater than

_____

C.

With 95% confidence, you can say that the population variance is between

___ and ___

D.

With 95% confidence, you can say that the population variance is less than

______

question 2

In a random sample of 23 people, the mean commute time to work was 31.6 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use at-distribution to construct a 99% confidence interval for the population mean . What is the margin of error of ? Interpret the results.

The confidence interval for the population mean is ___,___

(Round to one decimal place asneeded.)

The margin of error of is ____

(Round to one decimal place asneeded.)

Interpret the results.

A.

It can be said that 99% of people have a commute time between the bounds of the confidence interval.

B.

With 99% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

C.

If a large sample of people are taken approximately 99% of them will have commute times between the bounds of the confidence interval.

D.

With 99% confidence, it can be said that the commute time is between the bounds of the confidence interval.

queestion 3

In a survey of 2512 adults, 1469 say they have started paying bills online in the last year.

Construct a99% confidence interval for the population proportion. Interpret the results.

A99% confidence interval for the population proportion is ___, ____

(Round to three decimal places asneeded.)

Interpret your results. Choose the correct answer below.

A.

With99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

B.

The endpoints of the given confidence interval show that adults pay bills online99% of the time.

C.

With99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

question 4

Which statistic is the best unbiased estimator for ?

The best unbiased estimated for is _____

question 5

For the same samplestatistics, which level of confidence would produce the widest confidenceinterval? Explain your reasoning.

Choose the correct answer below.

a. 90%, because as the level of confidencedecreases, zc increases.

b. 90%, because as the level of confidencedecreases, zc decreases.

c. 99%, because as the level of confidenceincreases, zc decreases.

d. 99%, because as the level of confidenceincreases, zc increases.

question 6

A researcher wishes toestimate, with 95% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 3% of the true proportion.

a) No preliminary estimate is available. Find the minimum sample size needed.

b) Find the minimum sample sizeneeded, using a prior study that found that 36% of the respondents said they think their president can control the price of gasoline.

c) Compare the results from parts(a) and(b).

(a) What is the minimum sample size needed assuming that no prior information isavailable?

n=

nothing

(Round up to the nearest whole number asneeded.)

(b) What is the minimum sample size needed using a prior study that found that 36% of the respondents said they think their president can control the price ofgasoline?

n=

(Round up to the nearest whole number asneeded.)

(c) How do the results from (a) and (b)compare?

A.

Having an estimate of the population proportion reduces the minimum sample size needed.

B.

Having an estimate of the population proportion has no effect on the minimum sample size needed.

C.

Having an estimate of the population proportion raises the minimum sample size needed.