1. What is the One Sample t-statistic?

The one sample t-statistic measures how many standard errors the sample mean is from the hypothesized population mean. It's used in hypothesis testing to determine if a sample comes from a population with a specific mean.

2. How Does the Calculator Work?

The calculator uses the one sample t-statistic formula:

Where:

• \( \bar{x} \) — Sample mean
• \( \mu_0 \) — Hypothesized population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The numerator measures the difference between the sample and hypothesized mean, while the denominator standardizes this difference by the standard error of the mean.

3. Interpretation of Results

Details: A larger absolute t-value indicates greater evidence against the null hypothesis. Compare the t-value to critical values from the t-distribution with n-1 degrees of freedom.

4. Using the Calculator

Tips: Enter the sample mean, hypothesized 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 one sample t-test?
A: When you want to compare a sample mean to a known or hypothesized population mean, especially when the population standard deviation is unknown.

Q2: What's the difference between z-test and t-test?
A: Use z-test when population standard deviation is known (rare in practice). Use t-test when you must estimate standard deviation from the sample.

Q3: What degrees of freedom are used?
A: For one sample t-test, degrees of freedom = n - 1 where n is sample size.

Q4: How large should my sample be?
A: t-tests work well with samples > 30. For smaller samples, the data should be approximately normally distributed.

Q5: What if my data are paired or I have two samples?
A: Use paired t-test for before/after measurements or two sample t-test for comparing independent groups.