1. What is Student's t-test?

The Student's t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. This calculator computes the t-statistic for a one-sample t-test comparing a sample mean to a known population mean.

2. How Does the Calculator Work?

The calculator uses the t-test formula:

Where:

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

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

3. Importance of t-test

Details: The t-test is fundamental in statistics for hypothesis testing, especially when dealing with small sample sizes where the 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-test?
A: Use when comparing means of normally distributed data with unknown population standard deviation, especially with small sample sizes (n < 30).

Q2: What's the difference between z-test and t-test?
A: Use z-test when population standard deviation is known (large samples), t-test when it's unknown (small samples).

Q3: How do I interpret the t-statistic?
A: Higher absolute t-values indicate greater difference from the population mean. Compare to critical t-values from t-distribution tables.

Q4: What are the assumptions of t-test?
A: Data should be normally distributed, observations independent, and continuous scale of measurement.

Q5: Can I use this for two-sample t-tests?
A: No, this calculator is for one-sample t-tests. Two-sample tests require different formulas.