Question

An automobile manufacturer has given its van a 38.8 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 260 vans, they found a mean MPG of 39.0. Assume the population standard deviation is known to be 2.1. Is there sufficient evidence at the 0.01 level to support the testing firm's claim?

Answer 1

The null and alternative hypothesis is ,

(Claim)

The test is two tailed test.

Since , the population standard deviation is known.

Therefore , use normal distribution.

The test statistic is ,

The critical values are , ; From Z-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : There is not sufficient evidence at the 0.01 level to support the testing firm's claim.