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

Answer: (129.04,130.96)

Step-by-step 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 :-

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

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

Answer 2

Answer:

125-135

Step-by-step 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.