Question

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 25 24 17 13 14 20 13 15 12 25 12 18 21 17 12 20 17 24 13 12 15 24 17 17 19 22 24 18 22 23 23 21 18 23 23 16 14 16 14 13 13 24 13 12 25 15 14 20 16 18 16 17 12 12 24 14 12 24 16 13 24 15 21 24 14 12 14 16 25 20 23 24 13 13 13 16 13 24 17 24 Click here for the Excel Data File Assume that μ1 is the mean longevity for Brand A and μ2 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. 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 σA2 = 4.7 and σB2 = 6.4. (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 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 c. At the 5% significance level, what is the conclusion? Do not reject H0, there is no evidence that the average life differs between the brands. Reject H0, there is no evidence that the average life differs between the brands. Do not reject H0, there is evidence that the average life differs between the brands. Reject H0, there is evidence that the average life differs between the brands

Answer 1

Assume that μ1 is the mean longevity for Brand A and μ2 is the mean longevity for Brand B.

brand A	brand B
25	24
17	13
14	20
13	15
12	25
12	18
21	17
12	20
17	24
13	12
15	24
17	17
19	22
24	18
22	23
23	21
18	23
23	16
14	16
14	13
13	24
13	12
25	15
14	20
16	18
16	17
12	12
24	14
12	24
16	13
24	15
21	24
14	12
14	16
25	20
23	24
13	13
13	16
13	24
17	24
17.075	18.45

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

H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0

b-1. Calculate the value of the test statistic.

Assume that σA2 = 4.7 and σB2 = 6.4. (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.)

Since the population variances are known we will use the Z-test.

Under Ho:

Our test statistic is given as:

Rounding final answer to 2 decimal places, Z = - 2.61

b-2. Find the p-value.

We look for 2.61 in the Standard Normal Distribution table and subtract the probability value from 1 since it is for less than probability.

p - value = 0.00453

p-value < 0.01

Since p - value < , we have sufficient evideince to reject Ho at 5% level of significance.

c. At the 5% significance level, what is the conclusion?

Reject H0, there is evidence that the average life differs between the brands