To answer this question, we first need to understand the hypotheses being tested. The Carter Motor Company is making a claim about the average mileage of its new sedan, the Libra, in the city. They claim that the Libra will average better than 26 miles per gallon.
1. The null hypothesis ([tex]\(H_0\)[/tex]) is typically a statement of no effect or no difference, which is something to test against. In this case, it represents the scenario where the average mileage is exactly 26 miles per gallon.
2. The alternative hypothesis ([tex]\(H_1\)[/tex]) reflects what the company is trying to prove, which is that the new sedan averages better than 26 miles per gallon. In statistical terms, "better than" translates to "greater than."
Therefore, let's frame these hypotheses using the symbol [tex]\(\mu\)[/tex] to represent the true average mileage.
- The null hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu = 26\)[/tex], asserting that the true average mileage is 26 miles per gallon.
- The alternative hypothesis ([tex]\(H_1\)[/tex]): [tex]\(\mu > 26\)[/tex], stating that the true average mileage is greater than 26 miles per gallon.
So, from the given options, the correct pair of hypotheses is:
[tex]\[ H_0: \mu = 26 \][/tex]
[tex]\[ H_1: \mu > 26 \][/tex]
Therefore, the correct choice is:
[tex]\[ H_0: \mu=26 \quad H_1: \mu>26 \][/tex]
