(Use Excel) A consumer advocate researches the length of life between two brands

Question

(Use Excel) 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.

Specify the competing hypotheses to test whether the average length of life differs between the two brands.

Using the appropriate commands in Excel, find the value of the test statistic. Assume that A2 = 4.9 and B2 = 5.9. 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.)

Brand A Brand B Brand A Brand B 13 22 19 12 24 15 12 25 18 25 25 24 15 14 24 12 17 20 17 25 25 25 20 23 12 15 14 24 12 16 20 12 20 16 21 23 18 13 17 22 17 24 20 23 13 15 19 17 16 16 15 13 17 24 14 17 25 20 25 25 12 20 15 23 16 18 18 13 24 22 18 13 17 20 24 20 15 18 12 22

Explanation / Answer

The statistical software output for this problem is:

Two sample Z hypothesis test:
1 : Mean of Brand A (Std. dev. = 2.2135944)
2 : Mean of Brand B (Std. dev. = 2.4289916)
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0

Hypothesis test results:

Hence,

a) H0: 1 2 = 0; HA: 1 2 0

Option A is correct.

b) z = -2.45

P - value = 0.0141

c) Do not reject H0, there is no evidence that the average life differs between the brands

Option D is correct.

Difference n1 n2 Sample mean Std. err. Z-stat P-value 1 - 2 40 40 -1.275 0.51961524 -2.4537386 0.0141

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