Question

a used car dealer says that the mean price of a 2008 honda cr - v is at least $20,500. you suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. is there enough evidence to reject the dealers claim at α = 0.05? assume the population isnormally distributed.
state the hypothesis of the given problem.
ho: μ > 20,500
h1: μ < 20,500
ho: μ ≥ 20,500
h1: μ < 20,500
ho: μ ≤ 20,500
h1: μ > 20,500
ho: μ < 20,500
h1: μ ≥ 20,500

Explanation:

Step1: Identify the claim

The dealer claims the mean price is at least \( \$20,500\), which is \( \mu\geq20500\). The suspect's claim (the alternative hypothesis) is the opposite of the dealer's claim.

Step2: Set up the hypotheses

The null hypothesis \(H_0\) is the statement being tested. The alternative hypothesis \(H_1\) is what we might believe if the null is rejected. Since we suspect the mean is less than \(20500\), \(H_0:\mu\geq20500\) and \(H_1:\mu < 20500\)

Answer:

\(H_0:\mu\geq20500\), \(H_1:\mu < 20500\) (the second option in the given choices)