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). (answer to the question is provided as needed.) a. z < -2.58, z > 2.58 b. z < blank c. z > blank (c) find the standardized test statistic z for μ₁ - μ₂. z = -1.09 (round to two decimal places as needed.) (d) decide whether to reject or fail to reject the null hypothesis. choose the correct answer below. a. fail to reject h₀. the standardized test statistic is not in a rejection region. b. reject h₀. the standardized test statistic is not in a rejection region. c. reject h₀. the standardized test statistic is in a rejection region. d. fail to reject h₀. the standardized test statistic is in a rejection region.

Explanation:

Step1: Identify Rejection Region

From part (a), rejection region is \( z < -2.58 \) or \( z > 2.58 \).

Step2: Compare Test Statistic

Test statistic \( z = -1.09 \). Check if \( -1.09 \) is in rejection region: \( -2.58 < -1.09 < 2.58 \), so not in rejection region. Thus, fail to reject \( H_0 \).

Answer:

A. Fail to reject \( H_0 \). The standardized test statistic is not in a rejection region.