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Eleven components were tested to failure. The ordered ages (in hours) at failure were: 71, 87,...

Eleven components were tested to failure. The ordered ages (in hours) at failure were: 71, 87, 102, 104, 106, 111, 113, 117, 143, 159. The test was stopped at 200 hours (leaving one “survivor”). Calculate the Laplace (trend) statistic and test its significance. Clearly state your hypothesis, and conclusion.

show all formulas and steps do not do in excel or mathlab

Math   Statistics-And-Probability   
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Answer #1

Our null hypothesis is H0 : There is no trend in the data set against Ha: There is a trend present in the data.

We have the test statistic as , Here

So T = 12.18188 > 1.96

So, we reject the null hypothesis at 5% level of significance and conclude that there is a trend present in the given data set.

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