Hypothesis Testing Online: t-Test, Z-Test, F-Test and Chi-Square
What is Hypothesis Testing?
Hypothesis testing draws statistical inferences about population parameters or distributions from sample data. You state a null hypothesis H0 (usually no difference or no effect) and an alternative H1, then compute the p-value of a test statistic: when the p-value is below the significance level α (usually 0.05), H0 is rejected and the difference is called statistically significant. Two error types matter: a Type I error (α) rejects a true null, while a Type II error (β) accepts a false null, and power = 1−β increases with sample size.
When to Use It
Use it to compare means, variances or proportions, validate process improvements, compare suppliers or shifts, check a mean against a specification, and assess distribution fit. It is the standard evidence for data-driven decisions in quality engineering. Choose the method by data type: continuous with known variance or large samples for Z, unknown variance for t, paired designs for paired t, variance comparison for F, and counts or contingency tables for chi-square.
How to Use It (Step by Step)
State the research question and write down H0 and H1 including the one-tailed or two-tailed direction, then select the test that matches your data type. Enter the sample data or summary statistics such as mean, standard deviation and sample size. The tool automatically computes the test statistic, degrees of freedom, p-value and confidence interval, and provides interpretation guidance.
Key Formulas / Example
One-sample t = (x̄ − μ0)/(s/√n), one-sample Z = (x̄ − μ0)/(σ/√n), chi-square goodness of fit χ² = Σ(O − E)²/E, and F = s1²/s2² for two variances. Example: a p-value below 0.05 rejects H0. Remember that statistical significance is not the same as practical significance: check effect size and confidence intervals, and use the sample size calculator to avoid underpowered studies.