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. At its peak after the most recent recession, that rate reached 45.1% in July 2011 but has been steadily declining since then to 20% in April 2018. 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 α = 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. Comment on the value of alpha chosen for this test.