Question

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. A universal testing machine was used to test the tensile strength. The sample data is below. a. Find point estimates of the thickness and tensile strength data. Compare with the specifications. b. Construct a 95% confidence interval for mean thickness. Draw conclusions regarding the specification relative to the confidence interval. c. Construct a 95% confidence interval for mean 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.

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
2.4575	4.7377
2.6724	4.3407
2.2738	4.9487
2.5392	4.4265
2.7956	4.3583
2.1228	4.5608
2.2055	4.8207
2.4359	4.7769
2.3353	5.2468
2.3238	4.8706
2.5267	4.5138
2.2146	4.4402
2.2699	4.6548

Answer 1