A consumer advocate researches the length of life between two brands of refriger
ID: 3183708 • Letter: A
Question
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. Use Table 1. mu 1 is the mean longevity for Brand A and mu 2 is the mean longevity for Brand B. Let Brands A and B represent populations 1 and 2. respectively. Specify the competing hypotheses to test whether the average length of life differs between the two brands. H_0: mu_1 = 0; H_A: mu_1 - mu_2 notequalto 0 H_0: mu_1 = 0; H_A: mu_1 - mu_2 0 Using the appropriate commands in Excel, find the value of the test statistic. Assume that sigma_A^2 = 4.6 and sigma_B^2 = 6.1. What is the p-value? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter "Test statistic" value in 2 decimal places and "p-value" in 4 decimal places.) At the 1% significance level, what is the conclusion? Do not reject H_0. there is no 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. Reject H_0. there is evidence that the average life differs between the brandsExplanation / Answer
Brand A
Brand B
14
13
24
17
21
15
24
21
16
14
18
25
16
20
13
16
15
18
16
21
22
25
15
24
22
21
22
21
24
20
23
18
21
24
17
21
17
23
18
25
25
13
14
12
25
25
13
20
16
25
13
25
20
23
15
21
14
24
22
16
16
18
14
19
25
17
23
24
17
22
19
14
21
17
17
23
14
16
19
18
Part a)
Ho: µ1 - µ2 = 0; HA: µ1 - µ2 ¹ 0 (first option)
Part b)
To find the test statistics and p-value we go to Data then Data Analysis. There we select z- Test: Two Sample for Means . We select the data set and then we put 0 for Hypothesized mean difference and for variances we place the required values. We get the excel output as below:
z-Test: Two Sample for Means
Brand A
Brand B
Mean
18.5
19.85
Known Variance
4.6
6.1
Observations
40
40
Hypothesized Mean Difference
0
z
-2.61
P(Z<=z) one-tail
0.004525
z Critical one-tail
1.644854
P(Z<=z) two-tail
0.0090
z Critical two-tail
1.959964
Test statistic -2.61
p-value .0090
Part c)
Reject Ho, there is evidence that the average life differs between the brands. (4th option)
(p-value is less than the level of significance (.0090 < .01); Ho, can be rejected)
Brand A
Brand B
14
13
24
17
21
15
24
21
16
14
18
25
16
20
13
16
15
18
16
21
22
25
15
24
22
21
22
21
24
20
23
18
21
24
17
21
17
23
18
25
25
13
14
12
25
25
13
20
16
25
13
25
20
23
15
21
14
24
22
16
16
18
14
19
25
17
23
24
17
22
19
14
21
17
17
23
14
16
19
18
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