t-test Calculator

A one-sample t-test compares a sample mean to a hypothesized value.

How the Math Works

The one-sample t-test uses the formula t = (mean - mu) / (s / sqrt(n)) to determine if your sample data significantly differs from a hypothesized population mean (mu). Here, 'mean' is your sample average, 's' is the sample standard deviation, and 'n' is your sample size. The denominator (s / sqrt(n)) is the standard error, which measures how much your sample mean might vary from the true population mean. The resulting t-value tells you how many standard errors your sample mean is away from the hypothesized value - larger absolute t-values indicate greater evidence against the null hypothesis.

Practical Applications

To apply this test, first state your null hypothesis (typically that the population mean equals a specific value). Collect a random sample and calculate the sample mean and standard deviation. Input these values along with your hypothesized mean into the calculator. The tool will compute the t-statistic and corresponding p-value. If the p-value falls below your significance level (usually 0.05), reject the null hypothesis and conclude your sample provides significant evidence that the population mean differs from your hypothesized value.

Day-to-Day Use

This test helps you make data-driven decisions in everyday situations. For example, you could use it to verify if your monthly grocery spending truly averages $400 as your bank claims, or determine if a new diet supplement actually helps you lose weight beyond natural variation. It's valuable for quality control in businesses, evaluating whether product measurements meet specifications, or even in personal research like testing if your sleep hours differ significantly from the recommended 8 hours.

Worked example

mean 52, mu 50, s 6, n 30 gives t about 1.83, df 29.

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