Question

Four brands of light bulbs are being considered for use in the final assembly area of the Ford F-150 truck plant in Dearborn, Michigan. The director of purchasing asked for samples of 100 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.05 significance level, is there a difference in the quality of the bulbs? (Round your answers to 3 decimal places.) Manufacturer A B C D Unacceptable 19 13 19 10 Acceptable 81 87 81 90 Total 100 100 100 100

Answer 1

null hypothesis: Ho: there is no difference in the quality of the bulbs

Altrernative hypothesis: Ha: there is signficant difference in the quality of the bulbs

degree of freedom(df) =(rows-1)*(columns-1)=		3
for 3 df and 0.05 level , critical value       χ2=		7.8147
Decision rule : reject Ho if value of test statistic X2>7.815

Applying chi square test:

Expected	Ei=row total*column total/grand total	Small	Medium	Large	Large	Total
	unacceptable	15.25	15.25	15.25	15.25	61
	acceptable	84.75	84.75	84.75	84.75	339
	total	100	100	100	100	400
chi square    χ2	=(Oi-Ei)2/Ei	Small	Medium	Large	Large	Total
	unacceptable	0.922	0.332	0.922	1.807	3.9836
	acceptable	0.166	0.060	0.166	0.325	0.7168
	total	1.0881	0.3917	1.0881	2.1326	4.7004
test statistic X2 =		4.7004

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that there is a difference in the quality of the bulbs