Question

An automobile manufacturer has given its van a 37.2 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 performs over the manufacturer's MPG rating. After testing 260 vans, they found a mean MPG of 37.3. Assume the population standard deviation is known to be 2.3. Is there sufficient evidence at the 0.010.01 level to support the testing firm's claim?

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a right-tailed test, so the p-value is given by:

Since p-value is greater than 0.01, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus we cannot say that .