We're interested in the amount of time spent at work by college graduates employed full-time. The standard amount of time spent at work by full-time employees is40

hours per week. We suspect that the mean number

of hours worked per week by college graduates is less than40

hours and wish to conduct a statistical test. We select a random sample of75

college graduates employed full-time and compute the mean number of hours worked per week by the graduates in the sample.

Suppose that the population of hours worked per week by college graduates has a standard deviation of

4

hours and that we perform our hypothesis test using the0.1

level of significance.Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

What are the null and alternative hypotheses that we should use for the test?H

0

:

is

?less thanless than or equal togreater thangreater than or equal tonot equal toequal to?7539.1404H

1

:

is

?less thanless than or equal togreater thangreater than or equal tonot equal toequal to?7539.1404Assuming that the actual value of is 39.1 hours, what is the probability that we accept the null hypothesis? Round your response to at least two decimal places.

What is the probability that we commit a Type I error? Round your response to at least two decimal places.

Suppose that we decide to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test we use a significance level of 0.01 instead of a significance level of 0.1. Assuming that the actual value of is 39.1 hours, how does the power of this second test compare to the power of the original test?

The power of the second test is greater than the power of the original test

The power of the second test is less than the power of the original test

The powers of the two tests are equal