The average retirement age for French citizens between 2011 and 2016 was reported to be 59.7 years according to the Organization for Economic Cooperation and Development, an international group dedicated to promoting trade and economic growth. With the French pension system operating with a deficit, a bill was introduced by the government during the summer of 2010 to raise the minimum retirement age from 60 to 62. Suppose a survey of 40 retiring French citizens was recently taken to investigate whether the bill has raised the average age at which people actually retire. Assume the standard deviation of the retirement age is 5 years. Using α = 0.05, answer the following questions:

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

b. Calculate the probability of a Type II error occurring if the actual population age is 60 years old.

c. Calculate the probability of a Type II error occurring if the actual population age is 61.5 years old.