Question

A commonly used IQ test is scaled to have a mean of 100 and a standard deviation 15. A school counselor was curious about the average IQ of the students in her school and took a random sample of fifty students’ IQ scores. The average of these was 107.9. Find a 95% confidence interval for the student IQ in the school.

Answer 1

Answer: (103.74,112.06)

Step-by-step explanation:

The confidence interval for population mean is given by :_

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 50

Sample mean : $\overline{x}=107.9$

Standard deviation : $\sigma=15$

Significance level : $\alpha: 1-0.95=0.5$

Critical value : $z_{\alpha/2}=1.96$

Then the 95% confidence interval for the student IQ in the school will be :-

$107.9\pm (1.96)\dfrac{15}{\sqrt{50}}\\\\\approx107.9\pm0.075\\\\=(107.9-4.16,107.9+4.16)=(103.74,112.06)$

Hence, the 95% confidence interval for the student IQ in the school= (103.74,112.06)