Question

Carter Motor Company claims that its old sedan, the Libra, would average less than 19 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Answer 1

Null hypothesis:
`\mu \geq 19`

Alternative hypothesis:
`\mu < 19`

For this case after conduct the hypothesis test they conclude that that the conclusion is to reject the null hypothesis.

So then we can conclude that the true mean for this case is likely to be lower than 19 miles per gallon at some significance level who represent the error that can be present in this conclusion

Explanation:

When we conduct and hypothesis test the first step is find the system of hypothesis based on the claim.

For this case the objective is test the claim that the average less than 19 miles per gallon in the city (alternative hypothesis) and the complement should be the null hypothesis so then the system of hypothesis are:

Null hypothesis:
`\mu \geq 19`

Alternative hypothesis:
`\mu < 19`

For this case after conduct the hypothesis test they conclude that that the conclusion is to reject the null hypothesis.

So then we can conclude that the true mean for this case is likely to be lower than 19 miles per gallon at some significance level who represent the error that can be present in this conclusion