Question

According to Energy Information the average gas mileage of all automobiles is 21.4 miles per gallon. For a random sample of 40 sport utility vehicles, the mean gas mileage is 19.8 miles per gallon with a standard deviation of 3.5 miles per gallon. Test the claim that the mean mileage of all SUVs is different than the gas mileage of all automobiles.

a) z = 2.89 and a p value of .9938 .9938 < 0.05 There is not sufficient evidence to support the alternative hypothesis that the mean gas mileage of all SUVs is greater than 21.4 miles per gallon.

b) z = -2.89 and a p value of .0019 .0019 < 0.05 There is sufficient evidence to support the alternative hypothesis that the mean gas mileage of all SUVs is greater than 21.4 miles per gallon.

c) z = 2.89 and a p value of .9938 x 2 1.99 > 0.05 There is sufficient evidence to support the alternative hypothesis that the mean gas mileage of all SUVs is greater than 21.4 miles per gallon.

d) z = -2.89 and a p value of .0019 x 2 .0038 < 0.05 There is sufficient evidence to support the alternative hypothesis that the mean gas mileage of all SUVs is greater than 21.4 miles per gallon.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 21.4

H_a :    21.4

= 19.8

= 21.4

= 3.5

n = 40

Test statistic = z

= ( - ) / / n

= (19.8 - 21.4) / 3.5 / 40

= -2.89

Test statistic = -2.89

P(z < -2.89) = 0.0019

P-value = 2 * 0.0019 = 0.38

= 0.05

P-value <

Reject the null hypothesis .

d) z = -2.89 and a p value of .0019 x 2 .0038 < 0.05 There is sufficient evidence to support the alternative hypothesis that the mean gas mileage of all SUVs is greater than 21.4 miles per gallon.