1. What is the Test Statistic?

The test statistic measures how far a sample statistic deviates from what we would expect if the null hypothesis were true. It's used in hypothesis testing to determine whether to reject the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Sample Mean — Mean of your sample data
• Population Mean — Hypothesized population mean under null hypothesis
• SD — Standard deviation of the sample
• n — Sample size

Explanation: The formula standardizes the difference between the sample mean and population mean by the standard error of the mean.

3. Importance of Test Statistic

Details: The test statistic is crucial for determining statistical significance. It allows comparison of your results to what would be expected under the null hypothesis, helping decide whether observed differences are likely due to chance.

4. Using the Calculator

Tips: Enter all required values. The sample size must be at least 1, and standard deviation cannot be negative. The result can be positive or negative depending on whether the sample mean is above or below the population mean.

5. Frequently Asked Questions (FAQ)

Q1: What does a large test statistic value mean?
A: A larger absolute value indicates stronger evidence against the null hypothesis. The sign indicates direction of difference.

Q2: How is this related to p-value?
A: The test statistic is used to calculate the p-value, which determines statistical significance.

Q3: When is this formula appropriate?
A: This formula is appropriate when the sampling distribution is normal (large samples or normally distributed population).

Q4: What if my sample size is small?
A: For small samples (typically n < 30), you might need to use a t-distribution instead of normal distribution.

Q5: Can this be used for proportions?
A: For proportion tests, a different test statistic formula is used that accounts for the binomial nature of proportions.