Enter the sample mean, population mean, standard deviation of the population, and sample size into the calculator to determine the critical value Zc.

Critical Value Zc Formula

The following formula is used to calculate the critical value Zc.

Zc = X - μ / (σ / √n)


  • Zc is the critical value X is the sample mean μ is the population mean σ is the standard deviation of the population n is the sample size

To calculate the critical value Zc, subtract the population mean from the sample mean. Then, divide the standard deviation of the population by the square root of the sample size. Finally, divide the first result by the second result to get the critical value Zc.

What is a Critical Value Zc?

A critical value Zc is a statistical measurement used in hypothesis testing to determine whether to reject or fail to reject a null hypothesis. It is a threshold or cut-off point on the standard normal distribution curve, beyond which we reject the null hypothesis. The critical value is determined by the level of significance (typically 5%) and the type of test (one-tailed or two-tailed). It is denoted as Zc, where ‘Z’ represents the standard normal distribution and ‘c’ stands for critical.

How to Calculate Critical Value Zc?

The following steps outline how to calculate the Critical Value Zc using the formula:

  1. First, determine the sample mean (X).
  2. Next, determine the population mean (μ).
  3. Next, determine the standard deviation of the population (σ).
  4. Next, determine the sample size (n).
  5. Next, gather the formula from above: Zc = (X – μ) / (σ / √n).
  6. Finally, calculate the Critical Value Zc.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Sample mean (X) = 10

Population mean (μ) = 8

Standard deviation of the population (σ) = 2

Sample size (n) = 25