Question

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

minimum sample size = 97

Explanation:

Margin of error = 20

standard deviation = 100

sample size = n

standard error = 100/sqrt(n)

confidence level, alpha = 95%

Using the standard rule for 95% confidence

standard error <= sample mean
`\pm` 1.96 standard error, or

20 <= 1.96*100 / sqrt(n)

n >= (1.96*100/20)^2 = 9.8^2 = 96.04

=>

n >= 97