Question

The average retirement age for a certain country was reported to be 57.8 years according to an international group dedicated to promoting trade and economic growth. With the pension system operating with a? deficit, a bill was introduced by the government during the summer to raise the minimum retirement age from 60 to 62. Suppose a survey of 35 retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire. Assume the standard deviation of the retirement age is 5 years. Using alpha=0.05?, answer parts a through c below.

a. Explain how Type I and Type II errors can occur in this hypothesis test. A Type I error can occur when the researcher concludes the average retirement age increased, but the average retirement age did not increase. A Type II error can occur when the researcher concludes that the average retirement age did not increase, ?when, in? fact, the average retirement age increased.

b. Calculate the probability of a Type II error occurring if the actual population age is 59.1 years old. The probability of committing a Type II error is ___.

Answer 1

The Type I and Type II error statements are correct. We now need the Type II error, which is the probability of failing to reject a false null hypothesis.

This is a One-Tail Hypothesis test, in particular a Right-Tail.

Now we first need to calculate the critical mean value, corresponding to this significance level. That is,

Now the type II error is given by the probability to observe a sample mean less extreme than this critical value of 59.19, given that the actual mean equals 59.1. Hence,

The odds are more than one in half for a false negative.