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Dylan Jones kept careful records of the fuel efficiency of his new car. After the first eleven times he filled up the tank, he found the mean was 25.7 miles per gallon (mpg) with a sample standard deviation of 0.9 mpg. Compute the 95% confidence interval for his mpg

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Answer:
(25.1,\ 26.3)

Explanation:

As per given , we have


\overline{x}=25.7


s=0.9

n=11

df = 11-1=10

Since population standard deviation is unknown , so we use t-test.

Critical t-value :
t_(\alpha/2, df)=t_(0.025,10)=2.228

Confidence interval for population mean :_


\overline{x}\pm t_(\alpha/2)(s)/(√(n))\\\\=25.7\pm (2.228)(0.9)/(√(11))\\\\approx25.7\pm0.6\\\\= (25.7-0.6,\ 25.7+0.6)\\\\=(25.1,\ 26.3)

Hence, the 95% confidence interval for his mpg =
(25.1,\ 26.3)

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