Question

a manufacturer claims that his tires last at least 40,000 miles. a test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles. test the manufacturers claim at α =.01. what is the statement of the hypothesis of the given problem? ho: μ > 40,000 h1: μ < 40,000 ho: μ ≥ 40,000 h1: μ < 40,000 ho: μ ≤ 40,000 h1: μ > 40,000 ho: μ < 40,000 h1: μ ≥ 40,000

Explanation:

Step1: Identify the claim

The manufacturer claims that his tires last at least 40,000 miles. In hypothesis testing, the null hypothesis \(H_0\) is the statement of no difference or the claim we assume to be true initially. The alternative hypothesis \(H_1\) is the statement we are trying to find evidence for.

Step2: Set up the hypotheses

If the claim is \(\mu\geq40000\), then the null hypothesis \(H_0:\mu\geq40000\) (the claim we test against). The alternative hypothesis \(H_1:\mu < 40000\) (the opposite of the claim, what we might conclude if we reject the null hypothesis)

Answer:

\(H_0:\mu\geq40000\) and \(H_1:\mu < 40000\) (the second option in the given choices)