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)
