Question

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 is 40 hours per week. We suspect that the mean number μ of hours worked per week by college graduates is more than 40 hours and wish to do a statistical test. We select a random sample of 100 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 the 0.05 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.

(If necessary, consult a list of formulas.)

What are the null and alternative hypotheses that we should use for the test? H0:μis ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?10040.9404 H1:μis ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?10040.9404 What is the probability that we reject the null hypothesis when, in fact, it is true? Round your response to at least two decimal places. Assuming that the actual value of µ is 40.9 hours, what is the probability that we reject the null hypothesis? 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 0.05. Assuming that the actual value of µ is 40.9 hours, how does the probability that we commit a Type II error in this second test compare to the probability that we commit a Type II error in the original test? The probability of committing a Type II error in the second test is greater The probability of committing a Type II error in the second test is less The probabilities of committing a Type II error are equal

Answer 1

1)

null hypothesis:Ho		μ	is less than or equal to	40
Alternate Hypothesis:Ha		μ	is greater than	40

2)

probability that we reject the null hypothesis when, in fact, it is true =0.05

3)

probability that we reject the null hypothesis given actual value of µ is 40.9 hours =0.73

4)

The probability of committing a Type II error in the second test is greater