Question

# A consumer advocate researches the length of life between two brands of refrigerators, Brand A and...

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

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: μ1μ2 = 0; HA: μ1μ2 ≠ 0

• H0: μ1μ2 ≥ 0; HA: μ1μ2 < 0

• H0: μ1μ2 ≤ 0; HA: μ1μ2 > 0

b-1. Calculate the value of the test statistic. Assume that σA2 = 4.6 and σB2 = 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

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

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