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 population mean relative to the variability in the sample data.

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 t-statistic measures how many standard errors the sample mean is away from the population mean. A larger absolute t-value indicates a greater difference between the sample and population means.

3. Importance Of T-Statistic Calculation

Details: The t-statistic is crucial in determining whether to reject the null hypothesis in t-tests. It's widely used in research, quality control, and various scientific studies to make inferences about population parameters based on sample data.

4. Using The Calculator

Tips: Enter the sample mean, population mean, sample standard deviation, and sample size. All values must be valid (standard deviation > 0, sample size ≥ 2).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-test instead of a z-test?
A: Use a t-test when the population standard deviation is unknown and the sample size is small (typically n < 30). For larger samples, the t-distribution approximates the normal distribution.

Q2: What does a high t-value indicate?
A: A high absolute t-value (typically > 2) suggests that the difference between the sample mean and population mean is statistically significant, and you may reject the null hypothesis.

Q3: Can the t-statistic be negative?
A: Yes, the t-statistic can be negative when the sample mean is less than the population mean. The sign indicates the direction of the difference.

Q4: What are the assumptions for using the t-statistic?
A: The main assumptions are that the data are approximately normally distributed, observations are independent, and the sample is randomly selected from the population.

Q5: How is the t-statistic related to the p-value?
A: The t-statistic is used to calculate the p-value, which represents the probability of obtaining results as extreme as the observed results, assuming the null hypothesis is true.