Question

Salaries of 39 college graduates who took a statistics course in college have a​ mean, x​, of $ 61,600. Assuming a standard​ deviation, sigma​, of ​$17,362​, construct a 95​% confidence interval for estimating the population mean, μ.

Answer 1

Answer: (56150.92, 67049.08)

Explanation:

The confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))`

Given : Sample size :
`n=39`

Sample mean =
`\overline{x}=\$\ 61,600`

Standard deviation :
`\sigma=\$\ 17,362`

Significance level :
`1-0.95=0.05`

Critical value =
`z_(\alpha/2)=1.96`

Now, the 95​% confidence interval for estimating the population mean
`\mu`will be :-

`61600\pm (1.96)(17362)/(√(39))\\\\\approx61600\pm5449.08\\\\=(61600-5449.08,61600+5449.08)\\\\=(56150.92,\ 67049.08)`

Hence, the 95​% confidence interval for estimating the population mean = (56150.92, 67049.08)