3 Consider sampling from a population whose proportion of su

3.   Consider sampling from a population whose proportion of successes is p = 0.1. As the sample size, n, increases, some characteristics of the sampling distribution of p change. Which of the following characteristics will change as n increases, and what is the nature of the change?

a)

The mean of the sampling distribution of p

p will stay the same as the proportion

b)

The standard deviation of the sampling distribution of p

p will decrease as the proportion increases

c)

The shape of the sampling distribution of p

   The shape will become more normal as the proportion increases

Solution

The standard deviation of the sampling distribution of p, p will decrease as the proportion increases