1. Goodness of Fit Tests Qualitative (Nominal) Data
Counts of occurrences for each category (fi)
Null Hypothesis
Something that yields predicted number of expected count for each category (ei)
Test Statistic
2 = (fi-ei)2 / ei
Decision Rule
Reject H0 if 2 is “large” (2 > some 2 critical value)

2. Specific skewness depends on degrees of freedom
2 Distribution
Specific skewness depends on degrees of freedom
5 d.f
10 d.f
15 d.f

3. 2 Distribution
10 d.f
P(2 > ) = 0.05
P(2 < ) = 0.95 ?

4. 2 Distribution Critical Values
Degrees of Freedom
Area in Upper Tail
0.10
0.05
0.01
0.001 1
2.706
3.841
6.635
10.827 2
4.605
5.991
9.210
13.815 3
6.251
7.815
11.345
16.266 4
7.779
9.488
13.277
18.466 5
9.236
11.070
15.086
20.515 6
10.645
12.592
16.812
22.457 7
12.017
14.067
18.475
24.321 8
13.362
15.507
20.090
26.124 9
14.684
16.919
21.666
27.877 10
15.987
18.307
23.209
29.588

5. Equality of Percentages Example
An HR manager wants to know whether 30% of the workers are very satisfied, 30% are somewhat satisfied, 20% are indifferent, and 20% are quite unhappy with their jobs. It is your job to determine the answer, but you only have the resources to question 300 workers. What do you tell the HR manager (assume a 5% level of significance)?
From a random survey of 300 workers, you tabulate the following:
Number of workers
very satisfied 76
somewhat satisfied 100
indifferent 76
unhappy 48

6. Independent Events Example
You want to know whether race is related to the shift that the worker is working. An intern sample 228 workers in the factory and classifies them as follows:
Shift 1 Shift 2 Shift 3
White
Non-white
Can you conclude that race and shift are related (i.e., not independent)? (use  = 0.05)