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 H0 :μ = 4.0 versus H1 :μ ≠ 4.0.

a. Make a dotplot of the seven values.

b. Should a Student's t test be used to test H0? 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: 4.065, 3.967, 4.028, 4.008, 4.195, 4.057, and 4.010. Make a dotplot of these values.

d. Should a Student's t test be used to test H0 :μ ( 4.0 versus H1 :μ ( 4.0? If so, perform the test. If not, explain why not.