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?

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