Question

In a random sample of 1000 B.Com students 125 said that they wanted to become Statisticians. Assume the population of B Com students are normally distributed. Find the variance of the population proportion estimator

Answer 1

Step 1

Given;

$\begin{gathered} Total\text{ students=1000} \\ Random\text{ sample of students=125} \end{gathered}$

Step 2

Variance is given as;

$\begin{gathered} v=\sigma^2 \\ \sigma=\sqrt{\frac{pq}{n}} \\ \\ v=\frac{pq}{n} \end{gathered}$

where;

$\begin{gathered} p=success \\ q=1-success \\ n=sample\text{ size} \end{gathered}$$\begin{gathered} p=\frac{125}{1000}=0.125 \\ q=1-0.125 \\ q=0.875 \end{gathered}$$undefined$