Question

Four brands of lightbulbs 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 160 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?

Manufacturer A B C D Unacceptable 11 24 17 33 Acceptable 149 136 143 127 Total 160 160 160 160  

H0: There is no relationship between quality and manufacturer.

H1: There is a relationship.

A) State the decision rule using 0.05 significance level. (Round your answer to 3 decimal places.)

Reject H0 if chi-square >

B)Compute the value of chi-square. (Round your answer to 3 decimal places.)

Chi-square value

C) What is your decision regarding H0?

__ H0. There is ____ evidence to conclude that a relationship exists between quality and manufacturer.

Manufacturur

	A	B	C	D
Unacceptable	11	24	17	33
Acceptable	149	136	143	127
Total	160	160	160	160

Answer 1

This is a test of independence since we have to check whether the quality is independent of the manufacturer or not. We therefore use a chi-square test of independence.

	A	B	C	D	Total
Unacceptable	11	24	17	33	85
Acceptable	149	136	143	127	555
Total	160	160	160	160	640

The table for expected values is below

Eg: E(A|Acceptable) = =

E(A|unAcceptable) = =

	E(A)	E(B)	E ( C)	E(D)	Total
Unaccepetable	21.25	21.25	21.25	21.25	85
Acceptable	138.75	138.75	138.75	138.75	555
Total	160	160	160	160	640

Observed - expected

Eg: For A and unacceptable =

	A	B	C	D
Unacceptable	4.944118	0.355882	0.85	6.497059
Acceptable	0.757207	0.054505	0.13018	0.995045

= 14.584

A) State the decision rule using 0.05 significance level. (Round your answer to 3 decimal places.)

Reject H0 if chi-square > Critical value

Where C.V. =

r (row) = 2 c(column) = 4   = 0.05

= 7.81

Reject H0 if chi-square > 7.81

B)Compute the value of chi-square. (Round your answer to 3 decimal places.)

Chi-square value =

Chi-square value = 14.584

C) What is your decision regarding H0?

Since

_Reject_ H0. There is sufficient  evidence to conclude that a relationship exists between quality and manufacturer.