Stats homework please help

Question

An admissions director wants to estimate the mean age of all students enrolled at college. The estimate must be within 1 year of the population mean. Assume the population is normally distributed. Determine the minimum sample size required to construct a 95% confidence interval for the population mean assuming the population standard deviation is 2.7 years.

(a) 27 (b) 28 (c) 29 (d) 30

Answer 1

sample size = (z-critical * standard deviation/error) ^2

z-critical for 95% CI is found by looking up the z-score for a probability of 0.975, which is 1.96.

sample size = (1.96 * 2.7/1)^2 = 28 (b)