Question

A simple random sample of 400 individuals provides 100 Yes responses. a. What is the point estimate of the proportion of the population that would provide Yes responses? b. What is your estimate of the standard error of the proportion, p?

Answer 1

Answer: a.  0.25

b. 0.02165

Step-by-step explanation:

Given: sample size : n= 400

Number of individual respond Yes = 100

a. The proportion of the population respond Yes = $\dfrac{100}{400}=0.25$

Sample proportion is the best point estimate of the proportion of the population.

Hence, the point estimate of the proportion of the population that would provide Yes responses : p= 0.25

b. Standard error =  $\sqrt{\dfrac{p(1-p)}{n}}$

 $=\sqrt{\dfrac{0.25(1-0.25)}{400}}$

 $=\sqrt{\dfrac{0.25(0.75)}{400}}$

$=\sqrt{\dfrac{0.1875}{400}}$

$=\sqrt{0.00046875}=0.02165$

Hence, the estimate of the standard error of the proportion, p = 0.02165