Question

One gallon of gas is put into each of 30 test cars. The resulting gas-mileage values of the sample are computed with mean of 28.5 gallons per mile, and standard deviation of 1.2 miles per gallon. What is the 95% confidence interval estimate of the mean mileage?

Answer 1

Solution :

Degrees of freedom = df = n - 1 = 29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,29 = 2.045

Margin of error = E = t/2,df * (s /n)

= 2.045 * (1.2 / 30)

= 0.448

The 95% confidence interval estimate of the population mean is,

- E < < + E

28.5 - 0.448 < < 28.5 + 0.448

28.052 < < 28.948