Critical Value Calculator

Formula

The formula to calculate the critical value Zc is:

$\text{Zc} = \frac{X - \mu}{\left(\frac{\sigma}{\sqrt{n}}\right)}$

Where:

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

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.

Example Calculation

Example:

Sample Mean: 105
Population Mean: 100
Standard Deviation: 15
Sample Size: 30

Step 1: Calculate the critical value:

$\text{Zc} = \frac{105 - 100}{\left(\frac{15}{\sqrt{30}}\right)} \approx 1.83$