Question

an automobile manufacturer claims that their jeep has a 40.4 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this jeep. after testing 66 jeeps they found a mean mpg of 40.3 with a standard deviation of 1.4 mpg. is there sufficient evidence at the 0.1 level that the jeeps underperform the manufacturers mpg rating? state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is the manufacturer's claim. So $H_0:\mu = 40.4$.

Step2: Define alternative hypothesis

We want to test if the jeeps under - perform. So the alternative hypothesis $H_a:\mu<40.4$.

Answer:

$H_0:\mu = 40.4$
$H_a:\mu<40.4$