T-Test Calculator One Sample

One Sample T-Test Formula:

\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]

T-Value:

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1. What is a One Sample T-Test?

The one sample t-test determines whether the sample mean is statistically different from a known or hypothesized population mean. It's used when the population standard deviation is unknown and the sample size is relatively small (typically n < 30).

2. How Does the Calculator Work?

The calculator uses the one sample t-test formula:

\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]

Where:

\( \bar{x} \) — Sample mean
\( \mu \) — Population mean
\( s \) — Sample standard deviation
\( n \) — Sample size
\( t \) — Calculated t-value

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

3. Interpretation of Results

Details: The calculated t-value should be compared to critical values from the t-distribution table with n-1 degrees of freedom. A large absolute t-value suggests the sample mean is significantly different from the population mean.

4. Using the Calculator

Tips: Enter the sample mean, population mean, sample standard deviation (must be > 0), and sample size (must be ≥ 2). The calculator will compute the t-value which you can compare to critical values for hypothesis testing.

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 population mean and you don't know the population standard deviation.

Q2: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests check for a difference in one direction only, while two-tailed tests check for any difference (both directions).

Q3: How do I determine statistical significance?
A: Compare your t-value to critical values from the t-distribution table at your chosen significance level (typically 0.05).

Q4: What if my sample size is large?
A: For large samples (n > 30), the t-distribution approximates the z-distribution, but the t-test remains valid.

Q5: What are the assumptions of this test?
A: The data should be approximately normally distributed, observations should be independent, and the measurement scale should be continuous.