A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. These data are measured in years and can be found on the text website, labeled Refrigerator Longevity. Let Brands A and B represent populations 1 and 2, respectively. Use Table 1.
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
a.
Specify the competing hypotheses to test whether the average length of life differs between the two brands.
H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0
H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0
H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0
b.
Using the appropriate commands in Excel, find the value of the test statistic. Assume that σA2 = 4.6 and σB2 = 5.3. What is the p-value? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round “test statistic” value to 2 decimal places and “p-value” to 4 decimal places.)
Test statistic
p-value
c. At the 5% significance level, what is the conclusion?
Reject H0, the average life does not differ between the brands.
Do not reject H0, the average life differs between the brands.
Do not reject H0, the average life does not differ between the brands.
Reject H0, the average life differs between the brands.
