Question

# Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline...

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.

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :   = 50

Ha : > 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 .

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