Test Statistic Calculator

Step-by-Step Guide to Using the Test Statistic Calculator

Step 1: Enter Basic Information

Begin by filling in the Sample Size (n). This field accepts only whole numbers greater than 0. It represents the number of observations in your sample.

Step 2: Input the Sample and Population Data

• Enter the Sample Mean. This is the average calculated from your sample data.

• Provide the Population Mean (μ₀). This field requires the mean value of the population you are testing against.

• Enter the Sample Standard Deviation, which must be a non-negative number. This is the standard deviation calculated from your sample.

Step 3: Select the Test Type

Choose the appropriate Test Type for your hypothesis test. Options include:

• Two-tailed: Tests for significance in both directions.
• Left-tailed: Tests if the sample mean is significantly lower than the population mean.
• Right-tailed: Tests if the sample mean is significantly higher than the population mean.

Step 4: Specify the Significance Level

Input the Significance Level (α), which ranges from 0.001 to 0.999. This represents the probability of rejecting a true null hypothesis (Type I error).

Step 5: Calculate Results

Once all input fields are completed, the calculator will derive the following results:

• Standard Error: Computed as the standard deviation divided by the square root of the sample size.
• Test Statistic (z/t): Calculated using the formula (sample mean – population mean) divided by the standard error.
• Degrees of Freedom: Determined as the sample size minus one.
• Critical Value: Reflects the point beyond which we consider results statistically significant, depending on the test type.
• p-value: Indicates the probability of observing the test results under the null hypothesis. Calculation varies based on the selected test type.

Review the results to make conclusions about your hypothesis test.