Question

An auto maker estimates that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon. A random sample of 36 such vehicles had a mean of 18 miles per gallon and a standard deviation of 5 miles per gallon. At α = .01 can you reject the auto maker's claim?

Answer 1

Yes, we reject the auto maker's claim.

Explanation:

H0 : μ ≥ 20

H1 : μ < 20

Sample mean, xbar = 18 ;

Sample size, n = 36

Standard deviation, s = 5

At α = 0.01

The test statistic :

(xbar - μ) ÷ s /sqrt(n)

(18 - 20) ÷ 5/sqrt(36)

-2 /0.8333333

= - 2.4

Pvalue from test statistic : Pvalue = 0.00819

Pvalue < α

0.00819 < 0.01

Hence, we reject the Null