Question

A sample of 16 Math SAT scores for women was collected. The mean score for the sample was 463 and the sample standard deviation was 105. Find the 95% confidence interval for the population mean μ

μ. Assume the population has a normal distribution.

Answer 1

$n=16 \\ \bar{x}=463 \\ s=105$

the critical z-value is Zc = 1.96

$CI = (\bar{x} - \frac{Z_c \times s}{\sqrt{n}}, \bar{x} + \frac{Z_c \times s}{\sqrt{n}}) \\ CI = (463 - \frac{1.96 \times 105}{\sqrt{16}}, 463 + \frac{1.96 \times 105}{\sqrt{16}}) \\ CI = (463 - 51.45, 463 + 51.45) \\ CI = (411.55, 514.45)$