Benson Manufacturing is considering ordering electronic components from three di
ID: 3354570 • Letter: B
Question
Benson Manufacturing is considering ordering electronic components from three different suppliers. The suppliers may differ in terms of quality in that the proportion or percentage of defective components may differ among the suppliers. To evaluate the proportion defective components for the suppliers, Benson has requested a sample shipment of 500 components from each supplier. The number of defective omponents and the number of good components found in each shipment is as follows. Supplier Component Defective Good . Conduct a multiple comparison test to determine if there is an overall best supplier or if one supplier can be eliminated because of poor quality. Round p i, Pj and difference to two decimal places. Round 15 20 40 485 480 460 critical value to four decimal places. ComparisonP Pj Difference n jCritical Value Significant Diff> CvExplanation / Answer
A vs B 0.03 0.04 0.01 500 500 Zcritical = 1.96 at 5% significance. Z calculated = z=p¯(1p¯)(1/n1+1/n2)p^1p^2=0.035(10.035)(1/500+1/500)0.030.04=0.86 . Hence, not significant
A vs C 0.03 0.08 0.05 500 500 1.96
The z-statistic is computed as follows:
z = rac{hat p_1 - hat p_2}{sqrt{ ar p(1-ar p)(1/n_1 + 1/n_2)}} = rac{ 0.03 - 0.08}{sqrt{ 0.055cdot(1-0.055)(1/500 + 1/500)}} = -3.468z=p¯(1p¯)(1/n1+1/n2)p^1p^2=0.055(10.055)(1/500+1/500)0.030.08=3.468
(4) Decision about the null hypothesis
Since it is observed that |z| = 3.468 > z_c = 1.96z=3.468>zc=1.96, it is then concluded that the null hypothesis is rejected.
B vc C :
0.04 0.08 0.04 500 500 Zcritical=1.96;
Zcalculated=
The z-statistic is computed as follows:
z = rac{hat p_1 - hat p_2}{sqrt{ ar p(1-ar p)(1/n_1 + 1/n_2)}} = rac{ 0.04 - 0.08}{sqrt{ 0.06cdot(1-0.06)(1/500 + 1/500)}} = -2.663z=p¯(1p¯)(1/n1+1/n2)p^1p^2=0.06(10.06)(1/500+1/500)0.040.08=2.663
(4) Decision about the null hypothesis
Since it is observed that |z| = 2.663 > z_c = 1.96z=2.663>zc=1.96, it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is p = 0.0077p=0.0077, and since p = 0.0077 < 0.05p=0.0077<0.05, it is concluded that the null hypothesis is rejected.
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