A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The average thickness and the standard deviation of thickness for shift 1, based on a random sample of 37 gaskets, are 9.64 mm and 0.15 mm. The similar figures for shift 2, based on a random sample of 35 gaskets, are 9.66 mm and 0.18 mm. Let _{1 2} be the mean difference in thickness between shifts 1 and 2.

Calculate a 95% confidence interval for _{1 2}. Round your answers to three decimal places, if necessary.

Lower limit
Upper limit

Based on your answer to part a, are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1?

1. SelectDefinitely.Most likely.Probably, not.Definitely, not.Item 3

Explain.

Because the confidence interval extends from a SelectpositivenegativeItem 4 value to a SelectpositivenegativeItem 5 value, the population mean difference could be SelectpositivenegativeItem 6 .

How would your answers to parts a and b change if the sample sizes were instead 370 and 350?

We are Selectdefinitelymost likelyprobably notdefinitely notItem 7 convinced that the gaskets from shift 2 are, on average, wider than those from shift 1.