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

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 = 4.5 and σ_B² = 6.3. (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 :

.

H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

test statistic = -1.15

p-value > 0.10

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