1. What is the T Statistic?

The T Statistic is a value obtained from a t-test, used to determine if there is a significant difference between the means of two groups or between a sample mean and a theoretical mean.

2. How Does the Calculator Work?

The calculator uses the t statistic formula:

Where:

• \( \mu_{Observed} \) — Observed Mean of Sample
• \( \mu_{Theoretical} \) — Theoretical Mean of Sample
• \( s \) — Sample Standard Deviation
• \( N \) — Sample Size

Explanation: The formula calculates how many standard errors the observed mean is away from the theoretical mean.

3. Importance of T Statistic Calculation

Details: The t statistic is crucial for hypothesis testing in statistics, particularly in determining whether to reject the null hypothesis in various research studies and experiments.

4. Using the Calculator

Tips: Enter the observed mean, theoretical mean, sample standard deviation, and sample size. All values must be valid (standard deviation > 0, sample size ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between t statistic and z score?
A: The t statistic is used when the population standard deviation is unknown and the sample size is small, while the z score is used when the population standard deviation is known.

Q2: What is a good t statistic value?
A: There's no "good" or "bad" t statistic value. The significance depends on the degrees of freedom and the chosen alpha level (typically 0.05).

Q3: When should I use a one-sample t-test?
A: Use a one-sample t-test when you want to compare the mean of a single sample to a known value or theoretical mean.

Q4: What are the assumptions of the t-test?
A: The main assumptions are: the data is normally distributed, the observations are independent, and the data is measured at interval or ratio level.

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