Question

Suppose that we will randomly select a sample of n = 88 elements from a population and that we will compute the sample proportion of these elements that fall into a category of interest. If the true population proportion p equals .9: (a) Describe the shape of the sampling distribution of . Why can we validly describe the shape? (b) Find the mean and the standard deviation of the sampling distribution of . (Round the answers to 2 decimal places.)

Answer 1

a) Given that,

n = 88

p = 0.9

np = 88*0.9 = 79.2

n(1-p) = 88*0.1 = 8.8

Here, np and n(1-p) values are greater than 5.

Therefore, the sampling distribution of is normal distributed.

b)

Mean of the sampling distribution of

E() = p

= 0.9

standard deviation of sampling distribution of

= 0.03