A test was conducted to determine whether a wedge on the end of a plug fitting designed to hold a seal onto the plug was doing its job. The data taken were in the form of measurements of the force required to remove a seal from the plug with the wedge in place (say, X) and the force required without the plug (say, Y). Assume that the distributions of X and Y are N(μX, σ2) and N(μY, σ2), respectively. Ten independent observations of X are

Ten independent observations of Y are

(a) Find a 95% confidence interval for μX ˆ’ μY.
(b) Construct box-and-whisker diagrams of these data on the same figure.
(c) Is the wedge necessary?

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3.26 2.26 2.62 2.62 2.36 3.00 2.62 2.40 2.30 2.40 180 1.46 1.54 1.42 1.32 1.56 1.36 1.64 2.00 1.54