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.
Accepted Solution
A:
Answer: (56150.92, 67049.08)Step-by-step explanation:The confidence interval for population mean is given by :-[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]Given : Sample size : [tex]n=39[/tex]Sample mean = [tex]\overline{x}=\$\ 61,600[/tex]Standard deviation : [tex]\sigma=\$\ 17,362[/tex]Significance level : [tex]1-0.95=0.05[/tex]Critical value = [tex]z_{\alpha/2}=1.96[/tex]Now, the 95% confidence interval for estimating the population mean [tex]\mu [/tex]will be :-[tex]61600\pm (1.96)\dfrac{17362}{\sqrt{39}}\\\\\approx61600\pm5449.08\\\\=(61600-5449.08,61600+5449.08)\\\\=(56150.92,\ 67049.08)[/tex]Hence, the 95% confidence interval for estimating the population mean = (56150.92, 67049.08)