Question

A manufacturing company produces part QV2Y for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part QV2Y is the same for all three processes. The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, we performed a chi-square test to determine whether the quality of the items produced appears to be the same for all three processes. What is the null hypothesis?

H0: The proportion of defective units produced by the three production processes is the same.

Both "H0: The number of defectives produced is independent of the production process used." and "H0: The proportion of defective units produced by the three production processes is the same." are correct or at least acceptable ways of stating the null hypothesis.

All of the other choices are acceptable ways of stating the null hypothesis.

H0: The row and column variables are associated with each other.

H0: The number of defectives produced is independent of the production process used.

Answer 1

The hypothesis being tested is:

H0: The number of defectives produced is independent of the production process used.

Ha: The number of defectives produced is dependent on the production process used.

		Process 1	Process 2	Process 3	Total
Defective	Observed	29	12	9	50
	Expected	21.05	15.79	13.16	50.00
	O - E	7.95	-3.79	-4.16	0.00
	(O - E)² / E	3.00	0.91	1.31	5.22
Not Defective	Observed	211	168	141	520
	Expected	218.95	164.21	136.84	520.00
	O - E	-7.95	3.79	4.16	0.00
	(O - E)² / E	0.29	0.09	0.13	0.50
Total	Observed	240	180	150	570
	Expected	240.00	180.00	150.00	570.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	3.29	1.00	1.44	5.73
		5.73	chi-square
		2	df
		.0571	p-value

The p-value is 0.0571.

Since the p-value (0.0571) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the quality of the items produced appears to be the same for all three processes.

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