Chapter 8, Problem 21P

Research has shown that IQ scores have been increasing for years (Flynn, 1984. 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring from 10 years ago and plans to administers the test to a sample of $n=25$ of today’s high school students. Ten years ago, the scores on this IQ test produced a standardized distribution with a mean of $\mu =100$ and a standard deviation $\sigma =15$ . If there actually has been a 7-point increase in the average IQ during the past 10 years, then find the power of the hypothesis test for each of the following.

a. The researcher uses a two-tailed hypothesis test with $\alpha =.05$ to determine if the data indicate a significant change in IQ over the past 10 years.

b. The researcher uses a one-tailed hypothesis test with $\alpha =.05$ to determine if the data indicate a significant increase in IQ over the past 10 years.