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.

Answer 1

Answer: Required mean would be 15.

Step-by-step 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,

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

Hence, required mean would be 15.