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Used
to compare frequencies (counts) among multiple categories of nominal or ordinal level data
for one-sample (univariate analysis).
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 |
Assumptions
Independent
random sampling
Nominal
or Ordinal
level data
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
Determine
degrees of freedom (df) = k – 1 where
k equals the number of categories
df=5-1 or df=4
Establish
the confidence level (.05, .01, etc.)
Use
the chi-square distribution table to establish the critical value
At
alpha
.05 and 4 degrees of freedom, the critical value from the chi-square distribution is 9.488
Compute
the Test Statistic
where 
and
. . .
n
= sample size
k
= number of categories or cells
Fo
= observed frequency
|
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 cannot conclude there is a statistically significant difference among the assembly
lines in the observed frequencies of defective parts.
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