The number of long term unemployed, defined as those out of work for more than 27 weeks, has been a detriment to the recent economic recovery. In 2013, 40% of the unemployed had been out of work for more than 27 weeks. Government policy makers feel that this percentage has declined recently as the job market has improved. To test this theory, a random sample of 300 unemployed people was selected, and it was found that 112 were unemployed for longer than 27 weeks. Using σ = 0.10, answer the following questions:

a. Based on this sample, can the federal government conclude that the percentage of unemployed who have been out of work for more than 27 weeks has recently decreased?

b. Determine the p value for this test.

c. Use PHStat to validate these results.

d. Comment on the value of alpha chosen for this test.