Question

An automobile manufacturer claims that its van has a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 59.2. Assume the standard deviation is known to be 1.9. A level of significance of 0.1 will be used. Make a decision to reject or fail to reject the null hypothesis.

Make a decision.

Answer 1

To Test :-
H0 :- µ = 0
H1 :- µ ≠ 0

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 59.2 - 59.5 ) / ( 1.9 / √( 250 ))
Z = -2.4965 ≈ -2.50

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.1 /2 ) = 1.645
| Z | > Z( α/2 ) = 2.4965 > 1.645
Result :- Reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.1 level of significance
P value = 2 * P ( Z > 2.4965 ) = 2 * 1 - P ( Z < 2.4965 )
P value = 0.0125
Since 0.0125 < 0.1 ,hence we reject null hypothesis
Result :- Reject null hypothesis