Question

An automobile manufacturer claims that its van has a 55.955.9 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 270270 vans, they found a mean MPG of 56.056.0. Assume the standard deviation is known to be 1.11.1. A level of significance of 0.010.01 will be used. State the hypotheses.

Enter the hypotheses:

Answer 1

The null and alternative hypothesis

H0: = 55.9

Ha: 55.9

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 56 - 55.9 ) / ( 1.1 / √( 270 ))
Z = 1.49

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.01 /2 ) = 2.576
| Z | > Z( α/2 ) = 1.49 < 2.576

Result :- Fail to reject null hypothesis