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For one of the tasks in a manufacturing process, the mean time for task completion has historically been 35.0 minutes, with a standard deviation of 2.5 minutes. Workers have recently complained that the machinery used in the task is wearing out and slowing down. In response to the complaints, plant engineers have measured the time required for a sample consisting of 100 task operations. The 100 sample times, in minutes, re in data file XR09022. Using the mean for this sample, and assuming that the population standard deviation has remained unchanged at 2.5 minutes, construct the 95% confidence interval for the population mean. Is 35.0 minutes within the confidence interval? Interpret your “yes” or “no” answer in terms of whether the mean time for the task may have changed.

Formula:

CI95 = mean + or - 1.96(sd divided by √n)
...where + or - 1.96 represents the 95% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size.

CI95 = mean + or - 1.96 (2.5/√100)

Note: Determine the mean for the sample to be used in the above calculation.

Finish the calculation and determine the interval. Determine if the 35 minutes is contained within the interval.

I hope this will help get you started.

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