An article in Technometrics (1999, Vol. 41, pp.

202–211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data are shown below.

Paper Observations 1 3.481 3.448 3.485 3.475 3.472 3.477 3.472 3.464 3.472 3.470 3.470 3.470 3.477 3.473 3.474 2 3.258 3.254 3.256 3.249 3.241 3.254 3.247 3.257 3.239 3.250 3.258 3.239 3.245 3.240 3.254

(a) Check the assumption that the data from each sheet are from normal distributions.

(b) Test the hypothesis that the mean weight of the two sheets are equal against the alternative that they are not (and assume equal variances). Use and assume equal variances. Find the P-value.

(c) Repeat the previous test with

(d) Compare your answers for parts

(b) and

(c) and explain why they are the same or different.

(e) Explain how the questions in parts

(b) and

(c) could be answered with confidence intervals.