Answer: [tex](27.81,\ 29.39)[/tex]
Explanation:
Given : Sample size : n= 30 , it means it is a large sample (n≥ 30), so we use z-test .
Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Critical value: [tex]z_{\alpha/2}=1.96[/tex]
Sample mean : [tex]\overline{x}=28.6[/tex]
Standard deviation : [tex]\sigma=2.2[/tex]
The formula to find the confidence interval is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
i.e. [tex]28.6\pm (1.96)\dfrac{2.2}{\sqrt{30}}[/tex]
i.e. [tex]28.6\pm 0.787259889321[/tex]
[tex]\approx28.6\pm 0.79=(28.6-0.79,28.6+0.79)=(27.81,\ 29.39)[/tex]
Hence, the 95% confidence interval for the mean mpg in the entire population of that car model = [tex](27.81,\ 29.39)[/tex]
