Question

An automobile manufacturer claims that its van has a 33.7 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 230 vans, they found a mean MPG of 33.9 Assume the standard deviation is known to be 2.5. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis.

Make a decision.

Reject Null Hypothesis or Fail to Reject Null Hypothesis

Answer 1

Solution :

The null and alternative hypothesis is ,

H₀ :   = 33.7

H_a : 33.7

Test statistic (t)

= ( - ) / s / n

= (33.9 - 33.7) / 2.5 / 230

Test statistic = 1.21

P(z > 1.21) = 1 - P(z < 1.21) = 1 - 0.8869

P-value = 0.1131

= 0.02

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim that its van has a 33.7 miles/gallon rating.