# Homework Help: Hypothesis testing with nominal data.

1. Apr 5, 2007

### priit

1. The problem statement, all variables and given/known data

I have two variables (both nominal) union membership 1/0 and race 1/0 and I have to find if there is a relationship between them.
The task is formulated like so: "Is there a relationship between union membership and race (black versus non-black)?"
I know I have to state a null hypothesis and try to reject that.
What would be the easiest way to do that? I can define my own null hypothesis but I'm not even sure what could I test for this case?

2. Relevant equations
I have constructed following table from data:
Code (Text):

[   0] [   1]  TOT.

[   0]   854    63    917
[   1]   313    30    343

TOTAL 1167    93   1260

3. The attempt at a solution
I have calculated following test statistics from this table
Pearson chi-square test = 1,2853 (1 df, p-value = 0,256916)
and constructed few possible null hypothesis:
1) There are more white people in unions.
(By that I mean if in my data set would have equal distribution of black and white people then there would be more white union members than black.)
2) Union does not have equal distribution of black and white people. (That sounds a total nonsense somehow.)

And I have stated that I'll use a significance level of 0,05.
Comparing chi-square value with critical value from table I see it fits between upper and lower critical value so I can't reject null hypothesis.