A valve manufacturer produces a butterfly valve composed of two semicircular plates on a common spindle that is used to permit flow in one direction only. The semicircular plates are supplied by a vendor with specifications that the plates be 2.37 millimeters thick and have a tensile strength of five pounds per millimeter. A random sample of 20 such plates is taken. Electronic calipers are used to measure the thickness of each plate; the measurements are given here. Assuming that the thicknesses of such plates are normally distributed, use the data to construct a 95% level of confidence for the population mean thickness of these plates. Thickness Strength
2.4066 4.9175
2.1328 4.8067
2.5937 5.1246
2.1933 4.7555
2.4579 4.7233
2.0665 4.3934
2.1994 4.4609

Required:
a. Find point estimates of the thickness and tensile strength data. Compare with the specifications.
b. Construct a 95% confidence for thickness. Draw conclusions regarding the specification relative to the confidence interval.
c. Construct a 95% confidence for tensile strength. Draw conclusions regarding the specification relative to the confidence interval.
d. Construct a 95% confidence interval for the proportion of plates whose thickness is greater than the specification.