Question

A statistics student would like to estimate the average age of students at her college. She would like to be 99% confident that her estimate includes the actual college population mean. She did a smaller preliminary survey and found that a reasonable estimate of the population standard deviation was 2 1/2 years. How many people must she survey if she wants to be within 1/2 year of the true population mean?

Answer 1

Explanation:

Given that a statistics student would like to estimate the average age of students at her college.

Population std dev =2.5years

For 99% , Z critical = ±2.59

Margin of error =
`±2.59*(2.5)/(√(n) )  \\= (±6.475)/(√(n) ) =0.5`

Simplify to get

`√(n) =12.95`

n = 167.70

n=168

She must survey 168 people