Suppose that the population mean for IQ is 100 with a standard deviation of 15. A researcher is testing a group 25 of talented youth. His sample has a mean of 112 with a standard deviation of 14.
What does the CI tell us about the sample of young talented youth?
A) The youth have IQs comparable to that of the population
B) There is no evidence that the youth's IQ are higher than that of the general population
C) There is insufficient information to make any claims about the sample based on a 95% confidence interval.
D) The youth are indeed talented as their average IQ is significantly higher than that of the population at the alpha = .05 level

Question

Quizplus · Accepted Answer

The formula for the confidence interval is (sample mean - margin of error, sample mean + margin of error). Using the formula, we get (112 - 5.03, 112 + 5.03) which gives us the confidence interval of (106.97, 117.03). Since the population mean of 100 is not within this interval, we can reject the null hypothesis that the sample mean is not significantly different from the population mean. Therefore, the youth are indeed talented as their average IQ is significantly higher than that of the population at the alpha = .05 level.

Suppose That the Population Mean for IQ Is 100 with a Standard