State the question and method
Define the population and outcome. State both hypotheses and choose alpha before seeing the result. Explain the test choice, distinguishing independent groups from paired measurements.
Report evidence, then interpret it
Report sample size, descriptive statistics, test statistic, degrees of freedom and p-value. Add an effect estimate and confidence interval. Statistical significance alone does not establish practical importance.
Example
Invented one-sample classroom example, not an archive submission or observed study.
- Question
- Does mean task time differ from 50 minutes? H0: mean = 50; H1: mean differs from 50. Use a two-sided test at alpha = .05.
- Inputs and assumptions
- For 25 independent observations, mean = 52 minutes and sample SD = 10. Assume a roughly normal population with no influential outliers.
- Calculation
- Standard error = 10 / square root of 25 = 2. Thus t = (52 - 50) / 2 = 1.00, with 24 degrees of freedom; two-sided p is about .327.
- Write-up
- The sample did not provide sufficient evidence that the population mean differs from 50 minutes, t(24) = 1.00, p = .327. This does not prove that the mean equals 50.
Review your draft
Check assumptions, group labels, units and whether the p-value matches the planned one- or two-sided test. Report the analysis you ran, including limitations; do not switch hypotheses afterward to obtain significance.
Further reading: NIST: testing a population mean.
Past hypothesis-testing requests
Real historical request types, described without student text or files.
- Hypothesis-testing assignment — April 2021
- Hypothesis-testing request — March 2021
- Hypothesis-testing coursework — March 2021
- Hypothesis-testing and regression request — March 2021
Common questions
Does a large p-value prove the null hypothesis?
No. It means the test did not find sufficient evidence against that null at the chosen significance level. Sample size and uncertainty still matter.
Is a p-value the probability that the null is true?
No. It measures how unusual the result, or a more extreme result, would be under the null model and its assumptions.