1) According to an economicorganization, the weekly hours worked in manufacturing in a country was 42 hours in 2017. A recent random sample of 70 manufacturing workers in this country wasselected, and it was found that they worked an average of 38.8 hours last week with a sample standard deviation of 10.4 hours.

a. Using =0.10, is there enough evidence from this sample to conclude that the average number of manufacturing hours worked per week is different than 42 hours?

Determine the appropriate critical value. Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed. Use a comma to separate answers asneeded.)

A.

t=

B.

t/2=

C.

t=

Determine the test statistic.

tx=

(Round to two decimal places asneeded.)

State the conclusion.

Reject or not

------ evidence to conclude H0--------that the average number of manufacturing hours worked per week in this country-------- hours

(Type an integer or a decimal. Do notround.)

b. Thep-value i-------

(Round to three decimal places asneeded.)

2) During2016, the average monthly bill for digital cable in a country was $100. Suppose a cable company would like to test the hypothesis that the average monthly bill is higher than $100 this year. A random sample of 58 households was chosen. Assume the standard deviation of monthly cable bills in the country is $24. Complete parts a through d.

a. Explain how a Type I and Type II error can occur in this hypothesis test.

Explain how a Type I error can occur. Choose the correct answer below.

A.

The average monthly cable bill has changed from $100, but based on the sample it is incorrectly concluded that the average monthly cable bill has not changed from $100.

B.

The average monthly cable bill is greater than $100, but based on the sample it is incorrectly concluded that the average monthly cable bill is less than or equal to $100.

C.

The average monthly cable bill is equal to $100, but based on the sample it is incorrectly concluded that the average monthly cable bill has changed from $100.

D.

The average monthly cable bill is less than or equal to $100, but based on the sample it is incorrectly concluded that the average monthly cable bill is greater than $100.

Your answer is correct.

• Explain how a Type II error can occur. Choose the correct answer below.

A.

The average monthly cable bill has changed from $100, but based on the sample it is incorrectly concluded that the average monthly cable bill has not changed from $100.

Your answer is not correct.

B.

The average monthly cable bill is less than or equal to $100, but based on the sample it is incorrectly concluded that the average monthly cable bill is greater than $100.

C.

The average monthly cable bill is greater than $100, but based on the sample it is incorrectly concluded that the average monthly cable bill is less than or equal to $100.

This is the correct answer.

D.

The average monthly cable bill is equal to $100, but based on the sample it is incorrectly concluded that the average monthly cable bill has changed from $100.

b. Using =0.01, compute the probability of a Type II error occurring if the actual average monthly cable bill is $109.

The probability is

(Round to three decimal places asneeded.)

c. Using =0.10, compute the probability of a Type II error occurring if the actual average monthly cable bill is $109.

The probability is

(Round to three decimal places asneeded.)

d. Explain the differences in the results calculated in parts b and c. Choose the correct answer below.

A.

The value of is not affected by the value of .

B.

Increasing without changing the sample size will cause to increase.

C.

Increasing the sample size will reduce both and .

D.

Increasing without changing the sample size will cause to decrease.

3)

a. Explain how Type I and Type II errors can occur in this hypothesis test.

Explain how a Type I error can occur. Choose the correct answer below.

A.

The average wait time is less than 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time is greater than or equal to 1,419 seconds.

B.

The average wait time is equal to 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time has changed from 1,419 seconds.

C.

The average wait time is greater than or equal to 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time is less than 1,419 seconds.

Your answer is correct.

D.

The average wait time has changed from 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time has not changed from 1,419 seconds.

Explain how a Type II error can occur. Choose the correct answer below.

A.

The average wait time has changed from 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time has not changed from 1,419 seconds.

Your answer is not correct.

B.

The average wait time is equal to 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time has changed from 1,419 seconds.

C.

The average wait time is greater than or equal to 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time is less than 1,419 seconds.

D.

The average wait time is less than 1,419 seconds, but based on the sample it is incorrectly concluded that the average wait time is greater than or equal to 1,419 seconds.

This is the correct answer.

b. Using =0.10, compute the probability of a Type II error occurring if the actual average wait time per call is 1,325 seconds.

The probability is-----.

(Round to three decimal places asneeded.)

c. Using =0.10, compute the probability of a Type II error occurring if the actual average wait time per call is 1,258 seconds.

The probability is----.

(Round to three decimal places asneeded.)

d. Explain the differences in the results calculated in parts b and c. Choose the correct answer below.

A.

As the true population mean moves away from the hypothesizedmean, the power of the test decreases and decreases.

B.

As the true population mean moves away from the hypothesizedmean, the power of the test increases and decreases.

Your answer is correct.

C.

As the true population mean moves away from the hypothesizedmean, the power of the test increases and increases.

D.

As the true population mean moves away from the hypothesizedmean, the power of the test decreases and increases.