Question

443. An auto manufacturer claims that its new 4-cylinder Hybrid auto with manual shift averages 50 mpg under city driving conditions. A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturer's 4-cylinder Hybrid autos with manual shift. The Agency determines the mean average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions. At α = 5%, the conclusion of this hypothesis test is:

a. reject the null hypothesis and accept the alternative hypothesis
	b.	fail to reject the alternative hypothesis
	c.	accept both the null and alternative hypotheses
	d.	fail to reject the null hypothesis
	e.	reject the alternative hypothesis

Answer 1

To Test :-

H0 :- µ = 50
H1 :- µ < 50

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 48 - 50 ) / ( 4 / √(25) )
t = -2.50

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 25-1) = 1.711
t < - t(α, n-1) = -2.5 < - 1.711
Result :- Reject null hypothesis

a. reject the null hypothesis and accept the alternative hypothesis