Z Test Calculator

This Z Test Calculator allows users to perform hypothesis testing by calculating the Z-score, P-value, and determining whether to reject the null hypothesis based on provided sample and population data.

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How to Use the Z Test Calculator

This guide will walk you through the process of using the Z Test Calculator to perform hypothesis testing with step-by-step instructions.

Step 1: Input the Required Values

  1. Sample Mean: Enter the sample mean you have obtained from your data into the “Sample Mean” field. This is a required field.
  2. Population Mean (μ₀): Input the hypothesized population mean you are testing against in the “Population Mean” field. This is also required.
  3. Population Standard Deviation (σ): Provide the population standard deviation in the respective field. Ensure this value is greater than zero. This is required as well.
  4. Sample Size (n): Enter the size of your sample in the “Sample Size” field. This value should be a positive integer, with a minimum of 1.
  5. Significance Level (α): Choose a significance level from the dropdown menu. Options available are 0.10 (90% confidence), 0.05 (95% confidence), and 0.01 (99% confidence).

Step 2: Calculate the Test Statistics

Once you have entered all the necessary input data, the calculator will use the following formulas to determine key statistical metrics:

  • Z-Score: This is calculated using the formula: (Sample Mean – Population Mean) / (Population Standard Deviation / sqrt(Sample Size)).
  • P-Value (Two-Tailed): The p-value is calculated as 2 * (1 – normcdf(abs(zScore))), which tells you the probability of observing your results under the null hypothesis.
  • Critical Value: The critical value is computed using the formula: norminv(1 – significanceLevel/2), which determines the threshold for rejection of the null hypothesis.
  • Standard Error: This is calculated as Population Standard Deviation / sqrt(Sample Size), which measures the dispersion of the sample mean estimate.

Step 3: Interpret the Results

Based on the calculated metrics, interpret the results of the Z test as follows:

  • Test Result: The conclusion is drawn by comparing the Z-Score with the Critical Value. The decision is presented as either “Reject H₀” or “Fail to reject H₀” based on whether abs(zScore) > criticalValue.

This guide should help you effectively use the Z Test Calculator to hypothesize testing with the desired statistical confidence.