Question

Compute the length of the confidence interval for estimating the population

mean using a sample size of 300 and with a standard deviation 84. Use a 92%

confidence level.

Answer 1

According to the confidence interval formula

$a\in (x-Cr_{\alpha}*{\frac s {\sqrt n}},x+Cr_{\alpha}*{\frac s {\sqrt n}})$ , where a - estimated mean, x - sample mean, $Cr_{\alpha}$ - critical value at alpha confidence level, s - sample standard deviation, n - sample size

Since n is big(>30), then it is appropriate to use z-statistic as critical value, then

$P(Z>Cr)={\frac {1-{\alpha}} 2}=0.04\implies Cr=1.75$

so, $Cr_{\alpha}*{\frac s {\sqrt n}}=1.75*{\frac {84} {\sqrt {300}}}=8.487$

Then lenght of the confidence interval is 2*8.487=16.974