1. What is the T Score for Sample Mean?

The t score measures how many standard deviations the sample mean is from the population mean. It's used in t-tests to determine if there's a significant difference between sample and population means.

2. How Does the Calculator Work?

The calculator uses the t score 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 is from the population mean, while the denominator (standard error) scales this difference by the sample size.

3. Importance of T Score Calculation

Details: The t score is fundamental in hypothesis testing, particularly in determining whether observed differences between sample and population means are statistically significant.

4. Using the Calculator

Tips: Enter all values in consistent units. Sample size must be at least 1, and standard deviation must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between t score and z score?
A: T scores are used when population standard deviation is unknown (using sample SD) and/or with small sample sizes (<30).

Q2: What does a high t score indicate?
A: A higher absolute t value indicates greater difference between sample and population means relative to variability.

Q3: How is this related to p-values?
A: The t score is converted to a p-value using the t-distribution with n-1 degrees of freedom to test significance.

Q4: When should I use this formula?
A: For single sample t-tests comparing a sample mean to a known population mean.

Q5: What if my sample size is large?
A: For large samples (typically n>30), the t-distribution approximates the normal z-distribution.