Hypothesis Tests (Chi stastitic)?

Hypothesis Test (Chi Statistic)?


A study of the effects of the alphabetical listing of candidates in Irish elections obtained the following data. Test the null hypothesis that the candidates are random draws from all registered voters, without regard for surnames. Conduct a similar test of the null hypothesis that those elected are randomly drawn from all candidates without regard for surname.





A-C .203 91 47


D-G .179 63 32


H-L .172 59 23


M-0 .253 75 22


P-Z .194 47 20





The first column gives the fraction of the Irish voters who voted for those last names. The Second gives the number chosen as candidates, and the last how many were elected. I just need help with the first part.





Were the candidates chosen at randomn or not.





Hint: it will probably be helpful to transform the table into a cross-tabulation before analyzing the data.

Hypothesis Tests (Chi stastitic)?
As much as I prefer to write out the how's and whys of statistical testing, Wikipedia did a wornderful job with the chisquare test for independence. Here are two links to the how and why we use this this test.





for the candidates I get





Chi-squared test for given probabilities





data: candidates


X-squared = 16.7164, df = 4, p-value = 0.002194

















for the elected I get





Chi-squared test for given probabilities





data: elected


X-squared = 17.3194, df = 4, p-value = 0.001675





===





in both cases the very low p-values indicate we should reject the null hypothesis and conclude that no, the candidates and the elected members are not chosen at random.
Reply:Have not had to do this crap since college, so no need to start now. Sorry, this brought back horrid memories.