Answer:
Decison region :
Reject H0 : if χ² > 6.251
12.229
Step-by-step 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
