To estimate the average time it takes to assemble a certain computer component,

Question

To estimate the average time it takes to assemble a certain computer component, the industrial engineer at an electronics firm timed 64 technicians in the performance of this task, getting a mean of 12.50 minutes and a yariance of 4.00 minutes. (a) What can one assert with 98% confidence about the maximum error if 12.50 is used as a point estimate for the true average time it takes to assemble the computer component? (b) Construct a 98% confidence interval for the true average time it takes to assemble the computer component. (c) How large a sample is needed so that the engineer will be able to assert with confidence that the error is at most 0.3 minutes? (9 points)

Explanation / Answer

a)

Maximum error i.e. ME = 0.5816

This means true mean exists 0.5816 minutes within the mean with 98% probability.

b)

98% CI = (11.9184 , 13.0816 )

c)

CI for 98% n 64 mean 12.5 z-value of 98% CI 2.3263 std. dev. 2 SE = std.dev./sqrt(n) 0.25000 ME = z*SE 0.58159 Lower Limit = Mean - ME 11.91841 Upper Limit = Mean + ME 13.08159 98% CI (11.9184 , 13.0816 )

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