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 200 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.10 significance level, is there a difference in the quality of the bulbs?

Manufacturer
A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
1) State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.)
Reject H0 if chi-square >
2) Compute the value of chi-square. (Round your answer to 3 decimal places.)
Chi-square value

Answer 1

Decison region :

Reject H0 : if χ² > 6.251

12.229

Explanation:

Given :

Manufacturer A B C D

Unacceptable 29 17 9 22

Acceptable 171 183 191 178

Total 200 200 200 200

H0: There is no relationship between quality and manufacturer.

H1: There is a relationship.

Testing using the goodness of fit :

Chisquare = (observed - Expected)² / Expected

Expected Values:

19.25 19.25 19.25 19.25

180.75 180.75 180.75 180.75

Chi-Squared Values:

4.93831 0.262987 5.45779 0.392857

0.525934 0.0280083 0.581259 0.0418396

χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857

+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229

Degree of freedom, df = (4-1)(2-1) = 3*1= 3

The critical value,

χ² at 0.10, 3 = 6.251

Decison region :

Reject H0 : if χ² > 6.251

Reject H0 : 12.229 > 6.251