Question

an automobile manufacturer claims that their van has a 51.8 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 51 vans they found a mean mpg of 51.4 with a standard deviation of 2.1 mpg. is there sufficient evidence at the 0.1 level that the vans have an incorrect 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 statement of no - effect or the status - quo. Here, it is the manufacturer's claim. So, $H_0:\mu = 51.8$.

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is what we are trying to find evidence for. Since we want to test if the rating is incorrect (a two - tailed test), $H_a:\mu
eq51.8$.

Answer:

$H_0:\mu = 51.8$
$H_a:\mu
eq51.8$