question 7

The monthly incomes for 12 randomly selectedpeople, each with abachelor's degree ineconomics, are shown on the right. Complete parts(a) through(c) below.

Assume the population is normally distributed.

4450.91

4596.14

4366.25

4455.84

4151.47

3727.34

4283.78

4527.93

4407.11

3946.12

4023.61

4221.92

(a) Find the sample mean.

x=

(Round to one decimal place asneeded.)

(b) Find the sample standard deviation.

s=

(Round to one decimal place asneeded.)

(c) Construct a 90% confidence interval for the population mean .

A 90% confidence interval for the population mean is (__,__).

(Round to one decimal place asneeded.)

question 8

The waiting times(in minutes) of a random sample of 21 people at a bank have a sample standard deviation of 3.1 minutes. Construct a confidence interval for the population variance 2 and the population standard deviation . Use a 99% level of confidence. Assume the sample is from a normally distributed population.

What is the confidence interval for the population variance 2?

(

nothing

,

nothing

) (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 99% confidence, you can say that the population variance is greater than _____

B.

With 1% confidence, you can say that the population variance is less than _____

C.

With 99% confidence, you can say that the population variance is between

_____ and _____

.

D.

With 1% confidence, you can say that the population variance is between

____ and ____

What is the confidence interval for the population standard deviation ?

(____,___)

(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 1% confidence, you can say that the population standard deviation is between

_____ minutes and ______ minutes .

B.

With 99% confidence, you can say that the population standard deviation is less than

_____ minutes.

C.

With 99% confidence, you can say that the population standard deviation is between

_____ and ____minutes.

D.

With 1% confidence, you can say that the population standard deviation is greater than

_____ minutes

question 9

A soccer ball manufacturer wants to estimate the mean circumference ofmini-soccer balls within 0.10 inch. Assume the population of circumferences is normally distributed.

(a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.

(b) Repeat part(a) using a population standard deviation of 0.15 inch.

(c) Which standard deviation requires a larger samplesize? Explain.

(a) The minimum sample size with a population standard deviation of 0.25 inch is

____ balls.

(Round up to the nearestinteger.)

(b) The minimum sample size with a population standard deviation of 0.15 inch is

______ balls.

(Round up to the nearestinteger.)

(c) A population standard deviation of ________

inch requires a larger sample size because greater variability in the population requires a _____ sample size to ensure the desired accuracy.

question 11

You are given the sample mean and the population standard deviation. Use this information to construct the90% and95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. Ifconvenient, use technology to construct the confidence intervals.

A random sample of 60 home theater systems has a mean price of $127.00. Assume the population standard deviation is $15.60.

Construct a90% confidence interval for the population mean.

The90% confidence interval is (_____,____)

(Round to two decimal places asneeded.)

Construct a95% confidence interval for the population mean.

The95% confidence interval is (_____,_____)

(Round to two decimal places asneeded.)

Interpret the results. Choose the correct answer below.

A.

With90% confidence, it can be said that the sample mean price lies in the first interval. With95% confidence, it can be said that the sample mean price lies in the second interval. The95% confidence interval is wider than the90%.

B.

With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is narrower than the90%.

C.

With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is wider than the90%