1. The problem statement, all variables and given/known data We sample a population 50 times with replacement, with all individual sampled equally likely. We survey the gender and quality of life. The counts are: Male: 13 high quality, 11 low | female: 18 high, 8 low. Let P_M, P_F, P_H, P_L to denote these population proportions for each of the categories and let population proportions for the combinations be denoted by P_mh, P_ml, P_fh, P_fl. Paramaters are denoted by θ=(P_mh, P_ml, P_fh, P_fl). Null hypothesis: P_mh = P_m * P_h, P_ml = P_m * P_l... same for females Alternative hypothesis: P_mh =/= P_m * P_h, P_ml =/= P_m * P_l... same for females 1. Data counts are denoted by N_mh, N_ml, N_fh, N_fl. What is the joint probability mass function for these counts? 2. Write down the sets w_0 and w_A so that null hypothesis is θ∈w_0 and alternative hypothesis is θ∈w_A. 2. Relevant equations 3. The attempt at a solution 1. So I know understand the problem wants us to find P[(N_mh, N_ml, N_fh, N_fl)=(n_mh, n_ml, n_fh, n_fl)]. But I'm a bit confused on the notation and how to answer this problem. 2. Once again I'm not sure I understand exactly how to approach this problem. Any help is greatly appreciated.