For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the researcher who first reported it (Flynn, 1984, 1999), and it means that psychologists must continuously update IQ tests to keep the population mean at µ = 100. To evaluate the size of the effect, a researcher obtained a 10-year-old IQ test that was standardized to produce a mean IQ of µ = 100 for the population 10 years ago. The test was then given to a sample of n = 64 of today's 20-year-old adults. The average score for the sample was µ = 107 with a standard deviation of σ = 12.
a. Based on the sample, is the average IQ for today's population significantly different from the average 10 years ago, when the test would have produced a mean of µ = 100? Use a two-tailed test with a = .01.
b. Make an 80% confidence interval estimate of today's population mean IQ for the 10-year-old test.