Question

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

Answer 1

Answer: $(25.1,\ 26.3)$

Step-by-step 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 :_

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

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