Hypothesis Testing
Hypothesis testing is the formal statistical framework used to test claims about population parameters. By comparing sample statistics against null expectations, researchers determine if observed differences are statistically significant or just random noise.
- significance check: Hypothesis testing evaluates if sample evidence deviates sufficiently from a null hypothesis to reject it.
- test statistics: Z-score or T-score measures the number of standard errors separating the sample mean from the null mean.
- p-value criterion: The p-value measures the probability of observing our results if the null hypothesis is true. Reject when p < alpha.
One-Sample Hypothesis Testing
| Symbol | Meaning & Description |
|---|---|
| z / t | Standardized test statistic |
| x̄ | Sample Mean |
| μ₀ | Null Hypothesized Mean |
| SE | Standard Error = s / √n |
SE = s / √n = 15 / √30 = 2.7386
z = (x̄ - μ₀) / SE = (105 - 100) ÷ 2.7386 = 1.8257
Test statistic = 0.06789. p-value = 1.8257
Hypothesis Testing Calculator Sandbox
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SE = s / √n = 15 / √30 = 2.7386
z = (x̄ - μ₀) / SE = (105 - 100) ÷ 2.7386 = 1.8257
Test statistic = 0.06789. p-value = 1.8257
Accepting the Null Hypothesis: If a p-value is greater than alpha (e.g. 0.05), we do not "prove" the null hypothesis is true. We simply "fail to reject" it due to insufficient evidence.
Hypothesis Testing Calculator
Perform one-sample z/t hypothesis testing and compute exact p-values.