Question

PROBLEM 4

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.

a.	With a 0.01 level of significance, conduct a hypothesis test to determine whether or not the new automobiles actually do average more than 42 miles per gallon.

b. Construct a 90% confidence for the average MPG for the new automobiles from Efficiency Company.   

Answer 1

H0: µ = 42

Ha: µ > 42

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 42.8 - 42 ) / ( 1.2 / √(36) )
t = 4

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)

Critical value t(α, n-1) = t(0.01 , 36-1) = 2.438
t > t(α, n-1) = 4 > 2.438
Result :- Reject null hypothesis

We have sufficient evidence to support the claim that he new automobiles actually do average more than 42 miles per gallon.

b)

90% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 36- 1 ) = 1.69
42.8 ± t(0.1/2, 36 -1) * 1.2/√(36)
Lower Limit = 42.8 - t(0.1/2, 36 -1) 1.2/√(36)
Lower Limit = 42.462
Upper Limit = 42.8 + t(0.1/2, 36 -1) 1.2/√(36)
Upper Limit = 43.138
90% Confidence interval is ( 42.462 , 43.138 )