Question

Automobiles manufactured by the Efficiency Company have been averaging 42 miles per gallon of gasoline in highway driving. It is believed that its new automobiles average more than 42 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 42.8 miles per gallon with a standard deviation of 1.2 miles per gallon. Show all work.

a. With a 0.05 level of significance using the critical value approach, test to determine whether or not the new automobiles actually do average more than 42 miles per gallon.
b. What is the p-value associated with the sample results? What is your conclusion based on the p-value?

Answer 1

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.

Explanation:

H0 : μ = 42

H1 : μ > 42

Sample size, n = 36

xbar = 42.8

Standard deviation, s = 1.2

The test statistic :

(xbar - μ) ÷ (s / sqrt(n))

(42.8 - 42) ÷ (1.2 / sqrt(36))

0.8 ÷ 0.2 = 4

Test statistic = 4

Zcritical at 95% for a one - tailed test (right tailed) = 1.645

Test statistic > Critical value ; 4 > 1.645

Since Test statistic > Critical value ; We fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.

The Pvalue :

P(Z < 4) = 0.99997

Since,

Pvalue > α

0.99998 > 0.05 ; We fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.