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).

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

(b) find the critical value(s) and identify the rejection region(s).
the critical value(s) is/are
(round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Identify Test Type

This is a two - tailed z - test for the difference between two population means (since the alternative hypothesis is \(H_{a}:\mu_{1}
eq\mu_{2}\)) with \(\alpha = 0.01\).

Step2: Find Critical Values

For a two - tailed test with \(\alpha=0.01\), we split the significance level into two tails. So \(\alpha/2=0.005\) and \(1 - \alpha/2 = 0.995\).
We look up the z - value in the standard normal distribution table (or use a calculator) such that \(P(Z < z_{\alpha/2})=0.995\) and \(P(Z < - z_{\alpha/2}) = 0.005\).
From the standard normal table, the z - value corresponding to a cumulative probability of \(0.995\) is approximately \(2.58\), and the z - value corresponding to a cumulative probability of \(0.005\) is approximately \(- 2.58\).

Answer:

\(-2.58, 2.58\)