At a small college somewhere on the East coast, 20% of the girls and 30% of the boys smoke at least once a week.Independent random samples of 75 girls and 100 boys are to be selected and the proportions of smokers in the samples are to be calculated.What is the mean of the sampling distribution of the difference in the sample proportion of girl smokers and the sample proportion of boy smokers?

Answer: Required mean would be 15.Step-by-step explanation:Since we have given that Number of girls G= 75Number of boys B= 100Probability that girls smoke = P₂ = 0.20Probability that girls don't smoke = P'₂=1-0.20=0.80Probability that boys smoke = P₁ = 0.30Probability that boys don't smoke = P'₁=1-0.30=0.70We need to find the mean of the sampling distribution of the difference in the sample proportion of girl smokers and boys smokers.So, it becomes,[tex]E[P_1-P_2]=E[P_1]-E[P_2]\\\\=B\times P_1-G\times P_2\\\\=100\times 0.30-75\times 0.20\\\\=30-15\\\\=15[/tex]Hence, required mean would be 15.