Answer: [tex](25.1,\ 26.3)[/tex]
Step-by-step explanation:
As per given , we have
[tex]\overline{x}=25.7[/tex]
[tex]s=0.9[/tex]
n=11
df = 11-1=10
Since population standard deviation is unknown , so we use t-test.
Critical t-value : [tex]t_{\alpha/2, df}=t_{0.025,10}=2.228[/tex]
Confidence interval for population mean :_
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}\\\\=25.7\pm (2.228)\dfrac{0.9}{\sqrt{11}}\\\\approx25.7\pm0.6\\\\= (25.7-0.6,\ 25.7+0.6)\\\\=(25.1,\ 26.3)[/tex]
Hence, the 95% confidence interval for his mpg = [tex](25.1,\ 26.3)[/tex]
