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 μ_{1} is the mean longevity for Brand A and μ_{2} 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.
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
H_{0}: μ_{1} − μ_{2} ≥ 0; H_{A}: μ_{1} − μ_{2} < 0
H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
b-1. Calculate the value of the test statistic. Assume that σ_{A}^{2} = 4.5 and σ_{B}^{2} = 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 < 0.01
c. At the 5% significance level, what is the
conclusion?
Reject H_{0}, there is evidence that the average life differs between the brands.
Reject H_{0}, there is no evidence that the average life differs between the brands.
Do not reject H_{0}, there is evidence that the average life differs between the brands.
Do not reject H_{0}, there is no evidence that the average life differs between the brands
The statistical software output for this problem is :
.
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
test statistic = -1.15
p-value > 0.10
Do not reject H_{0}, there is no evidence that the average life differs between the brands
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