Question

9. A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?

Answer 1

Answer: 97

Explanation:

Formula to compute the required sample size :

`n= ((\sigma* z_(\alpha/2))/(E))^2`

, where
`\sigma` = standard deviation

E= Margin of error

`z_(\alpha/2)` = Two tailed z-value.

Here, E= 20

`\sigma` = 100

For 95% confidence level:
`z_(\alpha/2)` =1.96

Required sample size:

`n=((100*1.96)/(20))^2\\\\=(5*1.96)^2\\\\=96.04\approx97`

Hence, the required sample size : 97