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For several years, researchers have noticed a regular year-by-year increase in the average IQ for the general population, known as the Flynn effect (Flynn, 1984, 1999). This phenomenon requires psychologists to continuously update IQ tests to maintain a population mean of 100.

To evaluate the size of this effect, a researcher used a 10-year-old IQ test standardized to produce a mean IQ of 100 for the population 10 years ago. The test was given to a sample of 64 of today’s 20-year-old adults. The average score for the sample was 107 with a standard deviation of 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 100? Use a two-tailed test with α = .01.

Answer :

A hypothesis test shows that with a z-score of 4.67 for the given data (significantly beyond the threshold for
alpha = .01), we reject the null hypothesis, indicating that the current average IQ is significantly higher than a decade ago, in line with the Flynn Effect.

Evaluating the Flynn Effect with a Hypothesis Test

To determine if today's average IQ is significantly different from the mean of 100 a decade ago, we conduct a hypothesis test for the given sample data. We have a sample mean (ar{x}) of 107, a population mean (
mu) of 100, a standard deviation (s) of 12, and a sample size (n) of 64. Using a two-tailed test with a significance level (
alpha) of .01, we calculate the z-score.

The z-test formula is:
z = (ar{x} -
mu) / (s /
sqrt{n})
Substituting the given values:
z = (107 - 100) / (12 /
sqrt{64}) = 7 / (12 / 8) = 56 / 12 = 4.67

Using a standard normal distribution table, we find that a z-score of 4.67 has a very small probability, which is less than the significance level of .01. Therefore, we reject the null hypothesis and conclude that the average IQ score of today's population is significantly higher than it was a decade ago. This supports the presence of the Flynn Effect.

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