According to the U. S. Department of Labor, 12.3% of the U. S. workforce was unionized in 2009. This percentage has declined steadily since the end of World War II, when more than a third of U. S. workers belonged to a union. Suppose the department would like to test the hypothesis that the proportion of union workers decreased in 2014 by randomly sampling 160 employees.

a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.

b. Using σ = 0.05, calculate the probability of a Type II error if the actual proportion of unionized employees in the workforce is 10%.

c. Using σ = 0.05, calculate the probability of a Type II error if the actual proportion of unionized employees in the workforce is 5%.

d. Explain the differences in the results you calculated in parts b and c.