Question

Ahmadi, 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 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.

a.	Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b.	Compute the test statistic.
c.	What is the p-value associated with the sample results and what is your conclusion? Let a = .05.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 50

H_a : > 50

Test statistic = z

= ( - ) / / n

= (51.5 - 50) / 4 / 64

= 3

P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013

P-value = 0.0013

= 0.05

P-value <

Reject the null hypothesis .