Hypothesis Test Calculator

1. Enter raw data, or switch to summary statistics and type the sample mean, standard deviation, and size.
2. Enter the hypothesized mean (μ₀) from your null hypothesis.
3. Choose the alternative hypothesis (two-tailed, right-tailed, or left-tailed) and your significance level α.
4. Read the test statistic, p-value, and the reject / fail-to-reject decision, with the rejection area shaded on the chart.

Hypothesis testing is a procedure for deciding whether sample data provides enough evidence to reject a claim about a population. You start with a null hypothesis (H₀), usually a statement of “no effect” or “no difference,” and an alternative hypothesis (H₁) that you are testing for.

• H₀ (null): the population mean equals the hypothesized value, μ = μ₀.
• H₁ (alternative): the mean is different, greater, or less than μ₀, depending on your test.

1. State the null and alternative hypotheses.
2. Choose a significance level α (commonly 0.05).
3. Compute the test statistic from your sample.
4. Find the p-value for that statistic under the null hypothesis.
5. Reject H₀ if the p-value is less than α; otherwise fail to reject it.

Use a z-test when the population standard deviation is known (or the sample is very large); the test statistic is compared to the standard normal distribution. Use a t-test when the population standard deviation is unknown and estimated from the sample; the statistic follows the t-distribution with n − 1 degrees of freedom.