Question

you want to buy a washing machine, and a salesperson tells you that the mean repair costs for model a and model b are equal. you research the repair costs. the mean repair cost of 23 model a washing machines is $212. assume the population standard deviation is $17. the mean repair cost of 20 model b washing machines is $219. assume the population standard deviation is $24. at α = 0.01, can you reject the salesperson’s claim? assume the samples are random and independent, and the populations are normally distributed. complete parts (a) through (e). (a) identify the claim and state h₀ and hₐ. what is the claim? a. the mean repair cost for model a is greater than model b. b. the mean repair costs for model a and model b are equal. c. the mean repair costs for model a and model b are different. d. the mean repair cost for model a is less than model b. let μ₁ be the mean repair cost for model a and let μ₂ be the mean repair cost for model b. what are h₀ and hₐ? a. h₀: μ₁ < μ₂ hₐ: μ₁ ≥ μ₂ b. h₀: μ₁ ≥ μ₂ hₐ: μ₁ < μ₂ c. h₀: μ₁ = μ₂ hₐ: μ₁ ≠ μ₂ d. h₀: μ₁ ≠ μ₂ hₐ: μ₁ = μ₂ e. h₀: μ₁ > μ₂ hₐ: μ₁ ≤ μ₂ f. h₀: μ₁ ≤ μ₂ hₐ: μ₁ > μ₂

Explanation:

For the claim: The salesperson says the mean repair costs for Model A and Model B are equal, so option B matches. For \(H_0\) and \(H_a\): The null hypothesis \(H_0\) should reflect the claim (equality), and the alternative \(H_a\) is the opposite (not equal). So \(H_0: \mu_1 = \mu_2\) and \(H_a: \mu_1
eq \mu_2\), which is option C.

Answer:

What is the claim? B. The mean repair costs for Model A and Model B are equal.
What are \(H_0\) and \(H_a\)? C. \(H_0: \mu_1 = \mu_2\); \(H_a: \mu_1
eq \mu_2\)