Question

. Each individual in a random sample of high school students was cross-classified with respect to both political views and marijuana usage, resulting in the data displayed in the accompanying two-way table. Do the data support the hypothesis that political views and marijuana usage are associated within the population? Test the appropriate hypotheses using a 1% significance level. Political View Never Uses Rarely Uses Frequently Uses Liberal 480 180 120 Conservative 215 50 15 Other 170 45 85 (a) State the appropriate hypotheses.

Answer 1

(a) Let pij be the proportion of members of the population belonging to simultaneously to the i th class of "Marijuana use" and the j th class of "Political view".

   and   are the marginal totals of the proportions of of 'Marijuana uses' and 'Political View' respectively.

Then the null hypothesis is:

and the alternative hypothesis is:

.