Question

an automobile manufacturer claims that their van has a 36.5 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 5 vans they found a mean mpg of 36.8 with a standard deviation of 2.4 mpg. is there sufficient evidence at the 0.05 level that the vans outperform 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 that the mean MPG is equal to the manufacturer - claimed MPG.
$H_0:\mu = 36.5$

Step2: Define alternative hypothesis

The alternative hypothesis ($H_a$) is that the mean MPG is greater than the manufacturer - claimed MPG since we want to test if the vans outperform.
$H_a:\mu>36.5$

Answer:

$H_0:\mu = 36.5$
$H_a:\mu>36.5$