Question

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A manufacturer of certain devices has an average manufacturing time of 8.7 hours per device. Said manufacturer has decided to use new procedures to optimize said times. In a sample of 41 devices chosen at random, he found an average manufacturing of 8.6 hours with a standard deviation of 1.23 hours. With this evidence, and using a level of significance of 0.24, is it possible to conclude that the use of these new procedures has made the manufacturing time of each device faster?

Answer 1

Ho: Null hypothesis: the new procedure didn't make device faster

Ha: Alternate hypothesis: the new procedure did make device faster

sample average = 8.6 hours

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Stdev = 1.23 hours

Population average = 8.7 hours

n = 41

The level of significance = .24

Lets calculate the test statistic = (Xbar-Mu)/(Stdev/sqrt(n)) = (8.6-8.7)/(1.23/sqrt(41))

= -0.521

The p-value associated with this is basically = P(Xbar < -0.521) =  0.30262

Since this is more than our value of significance .24, we conclude that we fail to reject the null hypothesis and say that the new procedure did not make the manufacturing time of each device faster