1. What is the T-Statistic?

The t-statistic is a ratio of the departure of an estimated parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test.

2. How Does the Calculator Work?

The calculator uses the t-statistic formula:

Where:

• \( \bar{x} \) — Sample mean
• \( \mu \) — Population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The numerator measures how far the sample mean deviates from the population mean, while the denominator standardizes this difference by the standard error of the mean.

3. Importance of T-Statistic

Details: The t-statistic is fundamental in determining whether to reject the null hypothesis in a t-test. It's used when sample sizes are small and population standard deviation is unknown.

4. Using the Calculator

Tips: Enter the sample mean, population mean, sample standard deviation, and sample size. All values must be valid (n > 0, s ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-statistic?
A: Use it when comparing sample means, especially with small sample sizes (n < 30) and unknown population standard deviation.

Q2: What's the difference between t-statistic and z-score?
A: t-statistic is used when population standard deviation is unknown (using sample s), while z-score uses known population standard deviation.

Q3: How does sample size affect the t-statistic?
A: As sample size increases, the t-distribution approaches the normal distribution (z-distribution).

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

Q5: How do I interpret the t-value?
A: Compare your calculated t-value to critical values from the t-distribution table based on your significance level and degrees of freedom.