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 ,

H_{0} :
= 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 .

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