Calculate t-statistics, p-values, and critical values for statistical hypothesis testing. Supports one-sample, two-sample independent (Student's and Welch's), and paired t-tests with step-by-step calculations.
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Perform t-tests to compare means and make statistical inferences. Calculate t-statistics, p-values, degrees of freedom, and critical values for one-sample, two-sample independent, and paired t-tests. Includes Welch's t-test for unequal variances with complete step-by-step calculations.
The t-test is a statistical hypothesis test used to determine if there is a significant difference between means. Developed by William Sealy Gosset under the pseudonym 'Student', it's used when sample sizes are small and population standard deviation is unknown. The test produces a t-statistic that follows the t-distribution, allowing us to calculate the probability (p-value) of observing our results if the null hypothesis is true.
One-Sample T-Test Formula
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Use a t-test when the population standard deviation is unknown and you're estimating it from sample data, which is most real-world situations. Use a z-test only when you know the true population standard deviation or have very large samples (n > 100). The t-test is more conservative and appropriate for smaller samples.