Quickly and accurately perform Z-Test calculations by entering specific values, data arrays, test direction (sides), and custom flags. This versatile calculator is suitable for statisticians, researchers, and students who require flexible data analysis tools.

Z-Test Calculator (Value, Array, Sides, Flag)

Z-Test Calculator

Calculate the z‑score and p‑value using a given value and an array of data.
\( z = \frac{\text{Value} – \bar{x}}{SD} \)

* Enter the observed value, a comma‑separated list of data, select the test type (one‑tailed or two‑tailed), and choose whether to use sample or population standard deviation.

Step 1: Enter Test Data

e.g., 100

Enter a list of numbers.

Select one-tailed or two-tailed test.

Select whether to use sample or population SD.

Formula: \( z = \frac{\text{Value} – \bar{x}}{SD} \)
Two-tailed: \( p = 2\left[1-\Phi(|z|)\right] \)
One-tailed: \( p = \begin{cases}1-\Phi(z), & z \ge 0,\\ \Phi(z), & z < 0.\end{cases} \)
\( \Phi(z)=0.5\left[1+\operatorname{erf}\left(\frac{z}{\sqrt{2}}\right)\right] \)

How to Use This Calculator:

  1. Enter Values or Data Array: Input individual sample values or an array of data points.
  2. Specify Test Sides: Select the direction for your hypothesis test (one-sided or two-sided).
  3. Set Custom Flags: Choose optional flags to tailor your results according to your analytical needs.
  4. Click Calculate: Obtain immediate statistical significance results.

Example Calculation:

If you have sample data points and wish to perform a two-sided Z-Test, simply input your array, select two-sided, apply necessary flags, and receive instant results, including p-values and significance levels.

Frequently Asked Questions:

  • What does a Z-Test determine? A Z-Test assesses the statistical significance between sample data and known population parameters.
  • When should arrays versus single values be used? Arrays are used for analyzing data sets, while single values test specific individual observations against a population mean.
  • What are flags used for in the calculator? Flags allow customization of results, such as setting confidence intervals or other output adjustments.

Interpreting Results:

  • P-value: Indicates the probability of obtaining the observed outcome assuming the null hypothesis is true. Low p-values (typically ≤ 0.05) suggest significant findings.
  • Interpretation Guide: Clearly outlines practical implications for statistical decisions based on your results.

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