1. What is the T-Statistic?

The t-statistic is a measure used in hypothesis testing that follows a t-distribution under the null hypothesis. It quantifies the difference between the sample mean and the hypothesized population mean in terms of the standard error.

2. How Does the Calculator Work?

The calculator uses the t-statistic formula:

Where:

• \( \bar{x} \) — Sample mean
• \( \mu_0 \) — Hypothesized population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The t-statistic measures how many standard errors the sample mean is from the hypothesized population mean.

3. Importance of T-Statistic Calculation

Details: The t-statistic is crucial for determining whether to reject the null hypothesis in t-tests. It's widely used in research, quality control, and various scientific fields to make inferences about population means.

4. Using the Calculator

Tips: Enter your data values as comma-separated numbers, and provide the hypothesized population mean (μ0). The calculator will compute the sample mean, standard deviation, and t-statistic.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-test?
A: Use a t-test when comparing a sample mean to a hypothesized population mean, especially when the population standard deviation is unknown and sample size is small (n < 30).

Q2: What's the difference between t-statistic and z-score?
A: Both measure how many standard errors a point is from the mean, but t-statistic uses sample standard deviation while z-score uses population standard deviation.

Q3: How do I interpret the t-value?
A: Larger absolute t-values indicate stronger evidence against the null hypothesis. The specific interpretation depends on degrees of freedom and chosen significance level.

Q4: What are degrees of freedom in t-tests?
A: For a one-sample t-test, degrees of freedom equal n-1, where n is the sample size. This affects the shape of the t-distribution.

Q5: Can I use this for paired or two-sample t-tests?
A: This calculator is designed for one-sample t-tests. Different formulas are needed for paired or two-sample comparisons.