Question

An admission director wants to estimate the mean age of all students at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages are normally distributed. Determine the minimum sample size to size to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.6 years.

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 1.5, σ = 1.6

The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.645 * 1.6/1.5)^2
n = 3.08

Therefore, the sample size needed to satisfy the condition n >= 3.08 and it must be an integer number, we conclude that the minimum required sample size is n = 4
Ans : Sample size, n = 4