Question

A Research Director of a certain university wants to replicate the result of the study 10 years ago with a standard deviation of 0.14. He wants to estimate the population mean to within an error of 0.04 of its true value. Using 95% confidence level, what is the sample size that he needs?

Answer 1

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} =1.96.$

$$E=z_c\times\dfrac{\sigma}{\sqrt{n}}\le0.04$$

$$n\ge(\dfrac{1.96\cdot0.14}{0.04})^2$$

$$n\ge48$$