Question

A car company claims that its compact model gets 31 miles per gallon. A government inspector tests 38 of the company cars and finds that the average mileage is 29.7 mpg with a standard deviation of 2.2 mpg. Test if the mileage found is significantly less than the mileage claimed by the company using α = 0.01. (show bell shaped graph)

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 31

H_a : < 31

Test statistic = t

= ( - ) / s / n

= (29.7 - 31) / 2.2 / 38

Test statistic = -3.64

df = 30

P-value = 0.0005

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the mileage found is significantly less

than the mileage claimed by the company using α = 0.01.