AcaStat Statistical Software

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Contents  Introduction Descriptive Hypothesis Tables Appendix

Example: Chi-Square Goodness-of-Fit Test

Problem: You wish to evaluate variations in the proportion of defects produced from five assembly lines. A random sample of 100 defective parts from the five assembly lines produced the following contingency table.
 

Line A
Line B
Line C
Line D
Line E
24
15
22
20
19

State the Hypothesis

Ho: There is no significant difference among the assembly lines in the observed frequencies of defective parts.

Ha: There is a significant difference among the assembly lines in the observed frequencies of defective parts.

 Set the Rejection Criteria df=5-1 or df=4

At alpha .05 and 4 degrees of freedom, the critical value from the chi-square distribution is 9.488

 Compute the Test Statistic
 
 
Line A
Line B
Line C
Line D
Line E
  
Fo
24
15
22
20
19
  
Fe (100/5=20)
20
20
20
20
20
.8
1.25
.2
0
.05
2.30
Decide Results of Null Hypothesis Since the chi-square test statistic 2.30 does not meet or exceed the critical value of 9.488, you would conclude there is no statistically significant difference among the assembly lines in the observed frequencies of defective parts.