Question

What sample size should be used if we would like to estimate the mean age of the college students at a particular campus with 95% confidence? We would like to be accurate to within three years, and we will assume the population is normally distributed with a standard deviation of 5.1 years.

Answer 1

Answer: 12

Step-by-step explanation:

The formula to find the sample size is given by:-

$n=(\dfrac{z_c\cdot \sigma}{E})^2$ , where $\sigma$ is the population standard deviation, $z_c$ is the z-value for the $(1-\alpha)$ confidence interval and E is the margin of error .

As per given , we have

Population standard deviation : $\sigma=5.1$

z-value for 95% confidence interval : $z_c=1.960$

Margin of error : E= 3

Then, the required minimum sample :-

$n=(\dfrac{(1.96)\cdot (5.1)}{3})^2\\\\\Rightarrow\ n=(3.332)^2=11.102224\approx12$

Hence, the required minimum sample size = 12