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 = 0.05.

Day of Week	M	Tu	W	Th	F
Nondefective	87	86	94	87	86
Defective	7	7	13	4	10

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


(ii) Find the p-value. (Give your answer bounds exactly.)
< p <

Answer 1

applying chi square test:

Observed	Oi	M	Tu	W	TH	F	Total
	non-defective	87	86	94	87	86	440
	defective	7	7	13	4	10	41
	total	94	93	107	91	96	481
Expected	Ei=row total*column total/grand total	M	Tu	W	TH	F	Total
	non-defective	85.99	85.07	97.88	83.24	87.82	440
	defective	8.01	7.93	9.12	7.76	8.18	41
	total	94	93	107	91	96	481
chi square    χ2	=(Oi-Ei)2/Ei	M	Tu	W	TH	F	Total
	non-defective	0.0119	0.0101	0.1538	0.1695	0.0376	0.383
	defective	0.1279	0.1085	1.6501	1.8195	0.4035	4.109
	total	0.140	0.119	1.804	1.989	0.441	4.492

a) test statistic =4.49

ii)

p value =0.343

bounds : 0.3 <p value <0.4