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Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the...

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Statistics

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

Two brands of components are compared by installing one of eachbrand randomly in the right and left sides of several randomlyselected machines and noting the total machine operation time (inminutes) until the component needs to be replaced. Can you concludethat Brand 1 has a better mean lifetime based on the databelow?

Machine1234567
Brand 136,92545,30036,24032,10037,21048,36038,200
Brand 234,31842,28035,50031,95038,01547,80033,215

Answer & Explanation Solved by verified expert
3.6 Ratings (521 Votes)

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(), x?d = 1608.1429

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

Sample size, n = 7

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

Ho : µd = 0    

H1 : µd > 0 (claim)

Test statistic:     

t = (x?d)/(sd/?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 < ?, Reject the null hypothesis.

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