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 is the 95% confidence interval of the mean?
A) 106.2 - 117.8
B) 82.6 - 141.4
C) 84.56 - 139.44
D) 104.7 - 119.3

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean can be calculated using the formula: mean ± (Z * (standard deviation / sqrt(n))), where Z is the Z-score for a 95% confidence level (approximately 1.96), the standard deviation is 14, and n (sample size) is 25. This calculation gives us 112 ± (1.96 * (14 / sqrt(25))), which simplifies to 112 ± (1.96 * 2.8) = 112 ± 5.488, resulting in a confidence interval of 106.512 to 117.488, which rounds to 106.2 to 117.8.

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