Specifications call for the wall thickness of two-liter polycarbonate bottles to average 4.0 mils. A quality control engineer samples 7 two-liter polycarbonate bottles from a large batch and measures the wall thickness (in mils) in each. The results are: 3.999, 4.037, 4.116, 4.063, 3.969, 3.955, and 4.091. It is desired to test \(H_{0}: \mu=4.0\) versus \(H_{1}: \mu eq 4.0\).

a. Make a dotplot of the seven values.

b. Should a Student's \(t\) test be used to test \(H_{0}\) ? If so, perform the test. If not, explain why not.

c. Measurements are taken of the wall thicknesses of seven bottles of a different type. The measurements this time are: \(4.004,4.225,3.924,4.052,3.975,3.976\), and 4.041. Make a dotplot of these values.

d. Should a Student's \(t\) test be used to test \(H_{0}: \mu=4.0\) versus \(H_{1}: \mu eq 4.0\) ? If so, perform the test. If not, explain why not.