Question

For a certain group of cancer patients we are interested in estimating the mean age of diagnosis. We would like a 95% confidence level.

Assume the population standard deviation is 12 years.

a. What sample size do you recommend for an interval width of 5 years?

b. What sample size do you recommend for an interval width of 2 years?

Answer 1

a)

Margin of error E = (Width of interval) / 2 = 5 / 2 = 2.5

Sample size = (Z/2 * / E)²

= ( 1.96 * 12 / 2.5)²

= 88.51

n = 89 (Rounded up to nearest integer)

b)

Margin of error E = (Width of interval) / 2 = 2 / 2 = 1

Sample size = (Z/2 * / E)²

= ( 1.96 * 12 / 1)²

= 553.19

n = 554 (Rounded up to nearest integer)