Question

7. Bastien, Inc, has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 6 miles per gallon. Using the p-value approach, test to determine whether or not the manufacturer's advertising campaign is legitimate. Usea 05. 15 points

Answer 1

Hypotheses to be tested:

$H_0: \mu \leq 50$

against

$H_1: \mu > 50$

Test statistic:

$t = \frac{\bar{X} - 50}{\sigma/\sqrt{n}} = \frac{51.5 - 50}{6/\sqrt{36}} = 1.5$

P-value = P(Z > 1.5) = 0.067

As p-value > 0.05, we fail to reject the null hypothesis. Hence, the campaign is not legitimate.