Question

For n = 121, sample mean = 96 and a known population standard deviation = 14, construct a 95% confidence interval for the population mean.

Answer 1

Solution :

Given that,

Sample size = n = 121

Z_$\alpha$/2 = Z0.025 = 1.96

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 1.96 * (14 / $\sqrt$ 121)

Margin of error = E = 2.5

At 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

96 - 2.5 < $\mu$ < 96 + 2.5

93.5 < $\mu$ < 98.5

(93.5, 98.5)