1. Inference for Tables
Chi-Square Tests
Ch. 11

2. Food for thought Hypothesis Conditions Formula
Think about how one could summarize all null and alternative hypothesis into words
Conditions
Think about what the conditions are for the inference using categorical data previously learned
Formula
Oh yeah, they gave us a formula chart

3. Chi-Square Test Basics
Ho: observed is the same as what expected
Ha: observed is different than expected
Formula:
Conditions:
Data is from a random sample/event.
All individual expected counts are at least 5
(sample size is large enough).

4. Chi-Square df =1

5. Chi-Square df =2

6. Chi-Square df =3

7. Chi-Square df =4

8. Chi-Square df =5

9. Chi-Square df =8

10. Chi-Square Goodness of Fit
The chi-square(c2) test for goodness of fit allows the observer to test if a sample distribution is different from the hypothesized population.
Ho: the sample distribution is the same as the expected distribution
Ha: the sample distribution is different from the expected distribution

11. The type of household for the U.S. population is shown below.
The following results are based on a random sample of the community from Dove Creek, Montana.
Is there sufficient evidence to conclude that Dove Creek is different than the rest of the United States? Test at the 0.02 level.

12. Chi-square goodness of fit (or χ2 GOF, for short)
Ho: the number of household types in Dove Creek is the same as the U.S.
Ha: they are different
Expected values table:

13. Chi-square goodness of fit (or χ2 GOF, for short)
Ho: the number of household types in Dove Creek is the same as the U.S.
Ha: they are different
Expected values table:

14. Chi-square goodness of fit (or χ2 GOF, for short)
Ho: the number of household types in Dove Creek is the same as the U.S.
Ha: they are different
Expected values table:
Given random sample.
Exp. counts > 5, ∴ large sample

15. Formula:
(no need to rewrite tables again)
df=# of categories – 1 = 4

16. Chi-Square Table
df=4
We reject Ho, since p-value<a there is enough evidence to believe the distribution of household type in Dove Creek is different than the U.S.