Instruction of online calculator

Calculate The Test Statistic z0

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Input Data

One-tailed or Two-tailed Hypothesis

Output

Introduction

The test statistic ( z0 ) is crucial in hypothesis testing. It measures how far the sample mean is from the hypothesized population mean, expressed in terms of standard error. The test can either be one-tailed or two-tailed, depending on the research question. Here’s how to calculate ( z0 ), with an example illustrating both test types.

How to Use an Online Calculator

  1. Select an Online “Calculate The Test Statistic z0”: Find a calculator for hypothesis testing. Make sure it has fields for the required inputs.
  2. Input the Following Values:
    • Sample Mean (x̄): The mean from your sample data.
    • Population Mean (μ): The hypothesized mean of the population.
    • Standard Deviation (σ): The known standard deviation of the population.
    • Sample Size (n): The number of observations in your sample.
  3. Choose the Test Type:
    • One-tailed test: Use this when your hypothesis predicts a specific direction (greater or less than the population mean).
    • Two-tailed test: Use this when your hypothesis looks for any difference, regardless of direction.
  4. Click Calculate: The calculator will compute ( z0 ) and provide the p-value to determine statistical significance.

Example

Scenario:

A company claims the average lifespan of their product is 50 hours. You want to test whether the average lifespan is different based on a sample. Assume the following values:

  • ( x̄ = 55 ) (Sample Mean)
  • ( μ = 50 ) (Population Mean)
  • ( σ = 10 ) (Standard Deviation)
  • ( n = 25 ) (Sample Size)

Steps to Calculate ( z0 ):

  1. Subtract the population mean from the sample mean: [ x̄ – μ = 55 – 50 = 5 ]
  2. Calculate the standard error: [ σ / n^0.5 = 10 / 5 = 2 ]
  3. Compute ( z0 ): [ z0 = (x̄-μ)/(σ/n^0.5) = 2.5 ]

Interpretation:

  • One-tailed test: In this case, the significance level corresponding to z0  and the p-value of z0 is reported. which are 0.99379 and 0.00621.
  • Two-tailed test: In this case, the significance level corresponding to z0  and the p-value of z0 is reported. which are 0.99379 and 0.01242.

The above analysis can be seen in the online calculator.

one-tailed test result:

two-tailed test result: