# Three proportions testing null hypothesis

I have the following question.

In a random sample of 250 people with low incomes, 155 are in favour of a new piece of legislation, while in random samples of 200 people with average incomes and 150 people with high incomes there are, respectively, 118 and 87 who favour the legislation. use a significance level of $\alpha=0.05$ to test the null hypothesis that the proportion of people favouring the legislation is the same for all three groups.

I know that $H_0:p_1=p_2=p_3$ for low, average and high incomes. And $H_1$ is just that they are not equal. I was thinking I would need to do a chi-squared test but I'm not sure how to do that, given that I only have the sample proportions.

Would I just take the actual number of people in favour from each income group and then use the sample proportions? I'm a bit confused. Any help would be really good. Thanks.

## 1 Answer

You're essentially doing a test of homogeneity of proportions.

You need to arrange it as a 2x3 table (3 income groups vs favour/oppose) of counts, on which you can do a chi-square.

[Note however, that income groups are ordered (on income); you may want to consider an alternative that would be sensitive to a difference of opinion related to that ordering. On the other hand if you have no a priori expectation that the response will be ordered monotonically in income, the chi-square should be fine as is.]