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brojesus111
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Homework Statement
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 females1. 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.
Homework Equations
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.