Question

The manager of an assembly process wants to determine whether or not the number of defective articles manufactured depends on the day of the week the articles are produced. She collected the following information. Is there sufficient evidence to reject the hypothesis that the number of defective articles is independent of the day of the week on which they are produced? Use α = 0.01.

Day of Week	M	Tu	W	Th	F
Nondefective	88	92	98	97	91
Defective	11	7	3	3	8

(a) Find the test statistic. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)

Answer 1

(a) The test statistic = 8.09

(ii) p-value = 0.0883

		Col 1	Col 2	Col 3	Col 4	Col 5	Total
Row 1	Observed	88	92	98	97	91	466
	Expected	92.64	92.64	94.51	93.57	92.64	466.00
	O - E	-4.64	-0.64	3.49	3.43	-1.64	0.00
	(O - E)² / E	0.23	0.00	0.13	0.13	0.03	0.52
Row 2	Observed	11	7	3	3	8	32
	Expected	6.36	6.36	6.49	6.43	6.36	32.00
	O - E	4.64	0.64	-3.49	-3.43	1.64	0.00
	(O - E)² / E	3.38	0.06	1.88	1.83	0.42	7.57
Total	Observed	99	99	101	100	99	498
	Expected	99.00	99.00	101.00	100.00	99.00	498.00
	O - E	0.00	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	3.61	0.07	2.01	1.95	0.45	8.09
		8.09	chi-square
		4	df
		.0883	p-value

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