Efficiently calculate Z-Test statistics using a specified sample value, known population mean, standard deviation (SD), and test direction (one-sided or two-sided). Ideal for quick and accurate hypothesis testing in research and educational settings.

Z-Test Calculator (Value, Mean, SD, Sides)

Z-Test Calculator

Calculate the z‑score and p‑value for a z-test using: $$ z = \frac{\text{Value} – \text{Mean}}{\text{SD}}. $$

* Enter the observed value, mean, standard deviation, and select one‑tailed or two‑tailed test.

Step 1: Enter Test Parameters

e.g., 100

e.g., 95

e.g., 10

Select whether the test is one-tailed or two-tailed.

Formula: \( z = \frac{\text{Value} – \text{Mean}}{\text{SD}} \)
For two-tailed: \( p = 2\Bigl[1-\Phi(|z|)\Bigr] \)
For one-tailed: \( p = \begin{cases}1-\Phi(z), & z\ge0,\\ \Phi(z), & z<0.\end{cases} \)

How to Use This Calculator:

  1. Enter Sample Value: Input the specific sample value for your analysis.
  2. Provide Mean and SD: Enter the known population mean and standard deviation.
  3. Select Test Side: Choose either a one-sided or two-sided hypothesis test.
  4. Click Calculate: Instantly view your statistical results, including the calculated Z-Test statistic and p-value.

Example Calculation:

If your sample value is 120, the population mean is 100, and SD is 10, select your preferred test direction and calculate to receive immediate statistical significance results.

Frequently Asked Questions:

  • When should I use this Z-Test calculator? Use this calculator when you have a specific sample value and know the population mean and standard deviation.
  • What does the test side option represent? The test side determines whether the hypothesis test is directional (one-sided) or nondirectional (two-sided).
  • How do I interpret the Z-Test statistic? A high absolute value typically indicates strong statistical significance, meaning your sample differs significantly from the population mean.

Interpreting Results:

  • Z-Test Statistic: Shows how many standard deviations the sample value differs from the population mean.
  • P-value: Indicates the probability of observing your result assuming the null hypothesis is true; low values (≤ 0.05) suggest significant results.

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