Question

A sample size of 200 is selected from a population of with p=.30

a) Expected value of p(dash on top)?

b) Std error of p(dash on top)?

c) Show sampling distribution of p(Dash on top)

d) What does the sampling distribution of p(dash on top) show

Answer 1

Given sample size n = 200

Population proportion p = 0.30

a) Expected value for sample proportion is

b) standard error is given by

c) np =200* 0.3 = 60>10 and nq = 200(1-0.3) =140 >10

The np and nq are greater than 10

The proportion is normally distributed with mean and standard deviation .

d) The sampling distribution shows that probbaility that the proportion is greater than 0.3 is 0.5 and less than 0.3 is 0.5 because the curve is bell curve and the middle value is mean which is 0.3 in this case.

About 99.97% of the data lies with in to

ie., 99.97% of the samples lie between 0.2676 to 0.3324