A group of researchers wanted to estimate the mean height of High School Students in college....

Question

A group of researchers wanted to estimate the mean height of High School Students in college. It is believed that the population standard deviation is 46.5 cm. How big is the sample size be so that the 95% confidence interval will be 5.4 cm from the population mean?

Answer 1

As we know the population standard deviation

margin of error = z σ / sqrt (n)

σ = 46.5

z = 1.96 (for a 95% confidence interval)

margin of error = 5.4

So you need to solve margin of error for n, then take the sample size to be the first integer > n.