Suppose that there are two binomial populations For the firs

Suppose that there are two binomial populations. For the first, the true proportion of successes is 0.3; for the second, it is 0.5. Consider taking independent samples from these populations, 40 from the first and 60 from the second.

a) Find the mean and the standard deviation of the distribution of p1 p2 .

b) Find the mean and the standard deviation of the distribution of p1 0.5 .

c) What is the smallest value of p2 we would reject H 0 : p2 = 0.5 at significance level

= 0.05 , for the alternate hypothesis HA : p2 > 0.5 ?

Solution