Question

A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data (measured in years) on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. These data are measured in years. (You may find it useful to reference the appropriate table: z table or t table)

Brand A	Brand B	Brand A	Brand B
25	21	18	19
15	15	24	19
24	15	17	17
24	19	18	22
12	24	19	19
25	19	18	25
20	21	23	22
19	19	12	15
24	19	24	15
12	15	18	24
18	20	25	15
19	23	17	12
15	19	14	23
14	13	13	25
14	17	16	21
22	14	21	23
12	17	13	24
21	17	20	16
13	14	20	13
19	16	20	25

Click here for the Excel Data File

Assume that μ₁ is the mean longevity for Brand A and μ₂ is the mean longevity for Brand B.

a. Select the competing hypotheses to test whether the average length of life differs between the two brands.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b-1. Calculate the value of the test statistic. Assume that σ_A² = 4.6 and σ_B² = 5.3. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

c. At the 5% significance level, what is the conclusion?

• Reject H₀, there is evidence that the average life differs between the brands.

• Reject H₀, there is no evidence that the average life differs between the brands.

• Do not reject H₀, there is evidence that the average life differs between the brands.

• Do not reject H₀, there is no evidence that the average life differs between the brands

Answer 1

The statistical software output for this problem is :

Option A is correct.

Test statistics = -0.70

P-value > 0.10

Do not reject H₀, there is no evidence that the average life differs between the brands