Read to Lead

Sample size and power calculation

Sample Size to estimate mean

  • STATISTICS
Sample size to estimate mean The minimum sample size required to estimate the population mean $\mu$ is $$ \begin{aligned} n &= \bigg(\frac{z*\sigma}{E}\bigg)^2 \end{aligned} $$ where $\sigma$ is the population standard deviation $z=z_{\alpha/2}$ is the critical value of $Z$ $E$ is the margin of error. Example 1 An efficiency expert wishes to determine the average time that it takes to drill three holes in a certain metal clamp. How large a sample will she need to be 90% confident that her sample mean will be within 15 seconds of the true mean?
2 min Read 1

Sample size to estimate proportion

  • STATISTICS
Sample size to estimate proportion The minimum sample size required to estimate the population proportion is $$ n =p*(1-p)\bigg(\frac{z}{E}\bigg)^2 $$ where, $p$ is the proportion of success, $z$ is the $Z_{\alpha/2}$ (critical value of $Z$), $E$ is the margin of error. Example 1 A survey of 1000 randomly selected registered U.S. voters found that 37% were in favor of the recent tax reform plan. A new survey is being proposed to estimate the true proportion in favor of the recent tax reform plan.
3 min Read 1

Sample size to test mean

  • STATISTICS
Sample size to test mean The minimum sample size required to test the hypothesis about the population mean $\mu$ is $$ \begin{aligned} n &= \bigg(\frac{z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2 \end{aligned} $$ where $ES=\dfrac{|\mu_1-\mu_0|}{\sigma}$ is the effect size, $\sigma$ is the population standard deviation, $\alpha$ is the level of significance, $1-\beta$ is the power of the test. Example A researcher wishes to test the hypothesis $H_0:\mu=94$ against $H_a:\mu=97$ at $0.05$ level of significance. The population standard deviation is $\sigma= 4.
1 min Read 0