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 components and the number of good components found in each shipment is as follows. Supplier Component 10 35 Good 490 465 455 a. Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. 1. Ho: P p2 p3 Choose correct answer from above choice HaNot all population proportions are equal b. Using a.05 level of significance, conduct the hypothesis test. What is the p-value? Use Table 12.4. The p-value is 1 less than or equal .05 τ What is your conclusion? Conclude that the three suppliers do not provide equal proportions of defective c c. 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 ρ i decimal places. and difference to two decimal places. Round critical value to four Comparison ρί Difference Critical Value Significant Diff CV A vs B Avs C B vs C Yes No

Answer 1

Proportion of defectives components:

$\hat p_A = \frac{10}{10+490} = 0.02$

$\hat p_B = \frac{35}{35+465} = 0.07$

$\hat p_C = \frac{45}{45+455} = 0.09$

Degree of freedom = (3-1)*(2-1) = 2

At $\alpha$ = 0.05 and df =2, critical value of chi square, $\chi^2_c$ = 5.991

Critical value for A vs B =

$CV_{AB} = \sqrt{\chi^2_c}*\sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A}+\frac{\hat p_B(1-\hat p_B)}{n_B}}$

$= \sqrt{5.991}*\sqrt{\frac{0.02(1-0.02)}{500}+\frac{0.07(1-0.07)}{500}} = 0.0319$

Critical value for A vs C =

$CV_{AC} = \sqrt{\chi^2_c}*\sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A}+\frac{\hat p_C(1-\hat p_C)}{n_C}}$

$= \sqrt{5.991}*\sqrt{\frac{0.02(1-0.02)}{500}+\frac{0.09(1-0.09)}{500}} = 0.0349$

Critical value for B vs C =

$CV_{BC} = \sqrt{\chi^2_c}*\sqrt{\frac{\hat p_B(1-\hat p_B)}{n_B}+\frac{\hat p_C(1-\hat p_C)}{n_C}}$

$= \sqrt{5.991}*\sqrt{\frac{0.07(1-0.07)}{500}+\frac{0.09(1-0.09)}{500}} = 0.0420$

Comparison	$p_i$	$p_j$	Difference	$n_i$	$n_j$	Critical value	Significant Diff> CV
A vs B	0.02	0.07	0.05	500	500	0.0319	Yes
A vs C	0.02	0.09	0.07	500	500	0.0349	Yes
B vs C	0.07	0.09	0.02	500	500	0.0420	No