using excel : Problem 3 A valve manufacturer produces a butterfly valve composed

Question

using excel :

Problem 3
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 (seen here: http://en.wikipedia.org/wiki/Butterfly_valve). 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 are found in the homework 2 spreadsheet. By hand.
a. Determine, with 95% confidence, if mean tensile strength is less than five pounds per millimeter. Use the critical value approach.
b. Are more than half of plates thicker than 2.37? Use the p-value approach with 95% confidence.

the data are here :

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

Explanation / Answer

a)

here test stat =(X-mean)/std deviaiton =(4.6939-5)/0.0573 =-5.3386

here level of significance =0.05

degree of freedom =n-1=20-1=19

from excel function critical value =-tinv(0.10,19) =-1.729

as test statistics is lower then critical value ; we reject null hypothesis and conclude with 95% confidence that mean tensile strength is less than five pounds per millimeter.

b) here n=20;

and number of plates having thickness more then 2.37 =9

therefore estimated proportion phat =9/20=0.45

for p=0.5 and n=20

therefore std error =(p(1-p)/n)1/2 =0.1118

hence test stat z=(phat-p)/std error =-0.4472

for above p value =1-normsdist(-0.4472)=0.6726

as p value is greater then 0.05 level of significance we can not reject null hypothesis

we do not have sufficient evidence to conclude that more than half of plates thicker than 2.37.

please revert for any clarification required as well for any help regarding excel functions

Strength 4.9175 4.8067 5.1246 4.7555 4.7233 4.3934 4.4609 4.7377 4.3407 4.9487 4.4265 4.3583 4.5608 4.8207 4.7769 5.2468 4.8706 4.5138 4.4402 4.6548 mean 4.6939 std deviation 0.2564 std error=s/(n)1/2 0.0573

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