Question

A random sample of 145 students is chosen from a population of 4,250 students. If the mean IQ in the sample is 130 with a standard deviation of 7, what is the 90% confidence interval for the students' mean IQ score?

Answer 1

125-135

Explanation:

The standard deviation is 7. This implies that the IQ scorings can be between 123 and 137. With a 90% confidence in these numbers, 125-135 is the closest interval to 90% confidence.

Answer 2

Answer: (129.04,130.96)

Explanation:

Given : Sample size : n= 145

Mean IQ in the sample :
`\overline{x}=130`

Standard deviation :
`\sigma=7`

Significance level :
`\alpha=1-0.9=0.1`

Critical value :
`z_(\alpha/2)=1.645`

The confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))\\\\=130\pm(1.645)(7)/(√(145))\\\\=130\pm0.96\\\\=(129.04,\ 130.96)`

Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)