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

Explanation:

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

`n=((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=(((1.96)\cdot (5.1))/(3))^2\\\\\Rightarrow\ n=(3.332)^2=11.102224\approx12`

Hence, the required minimum sample size = 12