1. Section 13.1 Chi-square Test for Goodness of Fit (GOF)
AP Statistics

2. What would it have been like to be a crew member on the Titanic?
The crew of the Titanic made up 40% of the people on board.
But 45% of the deaths were from the crew (685 of 1517 deaths were from the crew)
Did the crew pay a heavier cost?
AP Statistics, Section 13.1

3. AP Statistics, Section 13.1

4. What is a test statistic?
z, t are test statistics
In the previous example, z=3.975.
What if…
z=0?
z=5?
z=-3?
We can say that the test statistic is a measure of unusualness. The higher the value, the more unusual the value.
AP Statistics, Section 13.1

5. Percent Observed Expected On board Lost O-E (O-E)^2/E First class 329
15%
130
227.55
-94.51
41.81
Second Class
285
13%
166
197.21
-28.49
4.93
Third Class
710
32%
536
485.44
51.49
5.26
Crew
899
40%
685
606.80
71.51
10.07
2223
100%
1517
0.00
61.02
AP Statistics, Section 13.1

6. AP Statistics, Section 13.1

7. What new for Chi-squared GOF
No parameter of interest; rather a model describing the distribution amongst several categories.
H0: the model is good.
Ha: the model is not good.
No normality check; rather no expected counts lower than 1. No more than 20% of the expected counts lower than 5.
df=number of categories-1
AP Statistics, Section 13.1

8. The statistic for goodness of fit
The Chi-square test statistic measures how closely the observed data matches what is expected given a particular model
AP Statistics, Section 13.1

9. Step 3: Test Statistic
AP Statistics, Section 13.1

10. Observed Expected Count Percentage (O-E)^2/E Blue 24% Brown 13% Green
Observed
Expected
Count
Percentage
(O-E)^2/E
Blue
24% 
Brown
13% 
Green
16% 
Orange
20% 
Red
Yellow
14% 
AP Statistics, Section 13.1

11. Exercises
odd
AP Statistics, Section 13.1