# Thread: Proportions, Test for Independence

1. ## Proportions, Test for Independence

Question: A random sample of 50 Democrats, 50 Republicans, and 50 Independents were asked if they favored the return of more power and funds to the state by the federal government. If 40 Democrats, 32 Republicans, and 25 Independents favored the return of power and funds to the states, can we conclude at the 0.005 level of significance that the proportions of Democrats, Republicans, and Independents favoring the return of funds and power to the states are about equal?

I'm pretty sure that this is is "chi-squared test for independence" sort of problem, but I don't know how to set up a data table to do the preliminary calculations. Any suggestions would be wonderful. Thank you.

2. Originally Posted by strgrl
Question: A random sample of 50 Democrats, 50 Republicans, and 50 Independents were asked if they favored the return of more power and funds to the state by the federal government. If 40 Democrats, 32 Republicans, and 25 Independents favored the return of power and funds to the states, can we conclude at the 0.005 level of significance that the proportions of Democrats, Republicans, and Independents favoring the return of funds and power to the states are about equal?

I'm pretty sure that this is is "chi-squared test for independence" sort of problem, but I don't know how to set up a data table to do the preliminary calculations. Any suggestions would be wonderful. Thank you.
It is.

Data table:

.................Democrat .... Republican .... Independent | Total
-----------------------------------------------------|
Favour ...........40 ............... 32 ................. 25 ......| . 97
.................................................. ...................... |
Don't favour ... 10 ............... 18 ................. 25 ......| . 53
-----------------------------------------------------|-----
Total ............ 50 ............... 50 ................. 50 ...... | .150

I assume you can:

1. Calculate the expected cell frequencies (using the formula E(nij) = ri cj/150).

2. Calculate X^2.

3. Get the critical value of chi-square for 0.005 level of significance (did you mean 0.05, by the way?). Note that degrees of freedom = (2-1)(3-1) = 2.