Question

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 1

Answer: Required mean would be 15.

Explanation:

Since we have given that

Number of girls G= 75

Number of boys B= 100

Probability that girls smoke = P₂ = 0.20

Probability that girls don't smoke = P'₂=1-0.20=0.80

Probability that boys smoke = P₁ = 0.30

Probability that boys don't smoke = P'₁=1-0.30=0.70

We 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,

`E[P_1-P_2]=E[P_1]-E[P_2]\\\\=B* P_1-G* P_2\\\\=100* 0.30-75* 0.20\\\\=30-15\\\\=15`

Hence, required mean would be 15.