The duration of worker's unemployment seems to be increasing. Suppose that special federal funds are available for your state when the mean period of unemployment exceeds 40 weeks. As an economist with your state's department of labor, you want to test whether the mean period of unemployment is more than 40 weeks. A random sample of 60 unemployed persons reveals the following.
Sample Size = 60
Sample Mean = 41.7 weeks
Sample Standard Deviation = 6.1 weeks
Does the sample data provide sufficient evidence to conclude that the population mean period of unemployment is greater than 40 weeks (usinga= .05)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide sufficient evidence to conclude that the population mean period of unemployment is greater than 40 weeks (usinga= .05)?