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:
16, 16, 16, 12, 14, 20, 16, 19, 17, 18, 19, 16, 19, 15, 16, 15, 19, 19, 16, 20, 20, 21, 16, 18, 12, 21, 21, 14, 16, 18, 18, 17, 19, 20, 21, 18, 14, 19, 15, 17, 15, 15, 20, 18, 13, 13, 13, 16, 13, 16, 18, 18, 15, 15, 18, 14, 15, 19, 21, 15, 12, 17, 16, 20, 15, 18, 16, 23, 16, 16, 18, 15, 17, 16, 16, 16, 16, 20, 18, 17
Brand B:
16, 16, 16, 12, 14, 20, 16, 19, 17, 18, 19, 16, 19, 15, 16, 15, 19, 19, 16, 20, 20, 21, 16, 18, 12, 21, 21, 14, 16, 18, 18, 17, 19, 20, 21, 18, 14, 19, 15, 17, 15, 15, 20, 18, 13, 13, 13, 16, 13, 16, 18, 18, 15, 15, 18, 14, 15, 19, 21, 15, 12, 17, 16, 20, 15, 18, 16, 23, 16, 16, 18, 15, 17, 16, 16, 16, 16, 20, 18, 17
Assume that μ1 is the mean longevity for Brand A and μ2 is the mean longevity for Brand B.
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-1. Calculate the value of the test statistic. Assume that σA^2 = 4.4 and σB^2 = 5.2. (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.)