Question

Determine the minimum sample size required when you want to be 95​% confident that the sample mean is within one unit of the population mean and sigma=19.1. Assume the population is normally distributed.

A 95 % confidence level requires a sample size of __

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 1, σ = 19.1

The critical value for significance level, α = 0.05 is 1.96.

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 = (1.96 * 19.1/1)^2
n = 1401.45

Therefore, the sample size needed to satisfy the condition n >= 1401.45 and it must be an integer number, we conclude that the minimum required sample size is n = 1402 or 1401