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 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: 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 = 4.5 and σB2 = 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

The statistical software output for this problem is :

.

H0: μ1μ2 = 0; HA: μ1μ2 ≠ 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

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