Question

A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg). You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg. At α=0.025​, test the​ company's claim. Assume the population is normally distributed. State the appropriate hypotheses to test.

Answer 1

Answer:

Null Hypothesis, $H_0$ : $\mu \geq$ 21 miles per gallon​    

Alternate Hypothesis, $H_A$ : $\mu$ < 21 miles per gallon

Step-by-step explanation:

We are given that a car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg).

You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg.

Let $\mu$ = mean gas mileage for its luxury sedan

So, Null Hypothesis, $H_0$ : $\mu \geq$ 21 miles per gallon​    

Alternate Hypothesis, $H_A$ : $\mu$ < 21 miles per gallon​

Here, null hypothesis states that  the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg).

On the other hand, alternate hypothesis states that the mean gas mileage for its luxury sedan is less than 21 miles per gallon​ (mpg).

The test statistics that would be used here is One-sample t test statistics as we don't know about population standard deviation i.e;

                       T.S.  =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~ $t_n_-_1$

Hence, the above hypothesis is appropriate for the given situation.