Question

In a population of 1000 subjects 640 possess a certain characteristics.A sample of 40 subjects selected from this population has 24 subjects who possess the same characteristics.what are the value of the population and sample proportions.

Answer 1

$$\hat{p}=\dfrac{X}{n}=\dfrac{24}{40}=0.6$$

$$E[\hat{p}]=p=\dfrac{640}{1000}=0.64$$

$$\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.64(1-0.64)}{40}}$$

$$=0.024\sqrt{10}\approx0.0759$$

The value of the population proportion is $p=0.64.$

The value of the sample proportion is $\hat{p}=0.6.$