Question

An automobile manufacturer claims that its van has a 40.3 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 39.9 . Assume the standard deviation is known to be 2.4 . A level of significance of 0.05 will be used. Make a decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 40.3

H_a :    40.3

Test statistic = z

= ( - ) / / n

= (39.9 - 40.3) / 2.4 / 250

= -2.64

P(z < -2.64) = 0.0041

P-value = 0.0082

= 0.05

P-value <

Reject the null hypothesis .