Question

In a quality control test of parts manufactured at Dabco Corporation, an engineer sampled parts produced on the first, second, and third shifts. The research study was designed to determine if the population proportion of good parts was the same for all three shifts. Sample data follow.

Production Shifts

Quality	First	Second	Third
Good	285	368	176
Defective	15	32	24

b. If the conclusion is that the population proportions are not all the same, use a multiple comparison procedure to determine how the shifts differ in terms of quality? Round pi, pj, and difference to two decimal places.

Comparison	pi	pj	Difference	ni	nj	Critical Value
1 vs 2
1 vs 3
2 vs 3

Answer 1

p̅1=285/300 =	0.95
p̅2=368/400 =	0.92
p̅3=176/200 =	0.88
X2 =	5.991 (for 0.05 level and 2 degree of freedom)
As Criitcal value =√X2*√(p̅1*(1-p̅1)/n1+p̅2*(1-p̅2)/n2)

b)

						critical val
Comparison	pi	pj	|abs diff|	ni	nj	value	significant diff >CV
1 vs 2	0.95	0.92	0.03	300	400	0.0453	not significant difference
1 vs 3	0.95	0.88	0.07	300	200	0.0641	significant difference
2 vs 3	0.92	0.88	0.04	400	200	0.0653	not significant difference