# If sample mean is 85, population standard deviation is 8 and sample size is 64, construct a 95%...

## Question:

If sample mean is {eq}85 {/eq}, population standard deviation is {eq}8 {/eq} and sample size is {eq}64 {/eq}, construct a {eq}95 \% {/eq} confidence interval estimate for the population mean.

## Confidence Interval for the Mean:

In interval estimation, confidence interval gives upper and lower limits true population mean is most likely to lie at a stated level of confidence. Interval estimation is used to address challenge of point estimation where true population mean slightly differ with the point estimate. Interval estimation helps to capture this slightly difference and ensure 'maximum' accuracy is told.

Given that;

{eq}\bar X=85\\\sigma=8\\n=64 {/eq}

Use equation below to obtain 95% confidence interval for the population mean:

{eq}\displaystyle \left(\bar X\pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{64}}\right) {/eq}

The critical value that correspond to 95% level of confidence is 1.96:

{eq}\displaystyle \left(85\pm 1.96\times \frac{8}{\sqrt{64}}\right)\\(85\pm 1.96)\\(83.04, 86.96) {/eq} 