Question

Assume that a population data is normally distributed with standard deviation of 1.4. Determine the minimum sample size required when you want to be 99% confident that the sample mean is within two units of the population mean.

Answer 1

The following information has been provided: (1)Margin of Error E = 2 (2)Level of significance α=0.01 (3)Population Standard deviation σ =1.4 The critical value for the significance level α=0.01 is Zc =2.5758. This can be found by using either Excel or by using the normal probability table. The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error: Therefore, the sample size needed to satisfy the condition is n ≥ 3.2511, and it must be an integer number, we conclude that the minimum required sample size is