Question

Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the test statistic and P-value, make a decision, and write the interpretation in terms of the claim. For consistency, use a significance level of 0.05 for the problem.

Two brands of components are compared by installing one of each brand randomly in the right and left sides of several randomly selected machines and noting the total machine operation time (in minutes) until the component needs to be replaced. Can you conclude that Brand 1 has a better mean lifetime based on the data below?

Machine	1	2	3	4	5	6	7
Brand 1	36,925	45,300	36,240	32,100	37,210	48,360	38,200
Brand 2	34,318	42,280	35,500	31,950	38,015	47,800	33,215

Answer 1

Brand 1	Brand 2	Difference
36925	34318	2607
45300	42280	3020
36240	35500	740
32100	31950	150
37210	38015	-805
48360	47800	560
38200	33215	4985

Sample mean of the difference using excel function AVERAGE(), x̅_d = 1608.1429

Sample standard deviation of the difference using excel function STDEV.S() s_d = 2008.1474

Sample size, n = 7

Null and Alternative hypothesis: µ_d = Brand 1-Brand 2

Ho : µ_d = 0    

H1 : µ_d > 0 (claim)

Test statistic:     

t = (x̅_d)/(s_d/√n) = 2.1187    

df = n-1 = 6    

Critical value :     

Right tailed critical value, t_c = ABS(T.INV(0.05,6) ) = 1.943

p-value :     

Right tailed p-value = T.DIST.RT(2.1187,6) = 0.0392

Decision:     

p-value < α, Reject the null hypothesis.

There is enough evidence to conclude that Brand 1 has a better mean lifetime at 0.05 significance level.