One-Sample T-Test Calculator | Easy Math Tools
Easily perform a one-sample t-test online to compare a sample mean to a hypothesized population mean. Get your test statistic, p-value, and interactive visualization instantly.
Input Parameters
Enter your sample data and hypothesized mean to perform the t-test.
Results
Test Statistic (t):
P-value:
Interpretation: Based on the p-value and significance level, you can determine whether to reject the null hypothesis.
Visualization
Explore the t-distribution curve and the critical region based on your test statistic.
Understanding the One-Sample T-Test
The One-Sample T-Test is a statistical hypothesis test used to determine whether the unknown population mean is different from a specific value. It's frequently used in research to test if a sample mean significantly differs from a hypothesized or known population mean.
Formula: The test statistic is calculated as: $$ t = rac{\bar{x} - \mu_0}{s / \sqrt{n}} $$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
The p-value helps determine the statistical significance of the test. A small p-value (typically ≤ 0.05) suggests that the null hypothesis can be rejected.
Example Use Case: Suppose you want to test if the average height of students in a university is different from 170cm. You collect a sample of student heights and perform a one-sample t-test to check if there's a significant difference.
For further reading, you can refer to resources like Wikipedia's article on Student's t-test.