--- title: "Setting Up a Hypothesis Test" description: "State a null and an alternative hypothesis about a population, fix a significance level before looking at the data, and decide in advance what result would count as surprising enough to reject the nul" canonical: https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf source: https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Setting Up a Hypothesis Test State a null and an alternative hypothesis about a population, fix a significance level before looking at the data, and decide in advance what result would count as surprising enough to reject the null. Subject: Mathematics · Area: Data & Statistics · Ages 17 to 18 Page: https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf ## Ready when they can - Write null and alternative hypotheses for a stated claim - Decide whether the test is one-tailed or two-tailed and say why - Describe a Type I error in the words of the question ## Lesson: Innocent until the data object Every test opens with two sentences about the population mean mu, never the sample. H0 is the neutral status quo with equals, such as mu = 5. H1 is the challenger: greater than, less than, or different from. Write both before touching data so the conclusion cannot drift. **Example.** For the claim a coin favours heads, H0 says p = 0.5 and H1 says p > 0.5. Favours points one way, so the test is one-tailed to the right with all of alpha in that tail. A farmer claiming eggs heavier than 60 g gets H1: mu > 60 the same way. The significance level alpha is the budgeted false alarm rate, commonly 0.05: if H0 is true, a 5% test still rejects it 5 times in 100. Type I is that false alarm, rejecting a true H0. Type II is the miss, keeping H0 while reality moved on. Always phrase errors in the words of the question. **Tip.** Differs in either direction means two tails sharing alpha evenly: level 0.10 puts 0.05 in each tail. Direction words pick the tail: greater than goes right, less than goes left, differs goes both. H0 stays the assumed truth until the data argue otherwise. **Recap.** Write H0 with equals about the population, pick the tail from the claim, and fix alpha before the data arrive. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Sampling Distributions and the Central Limit Theorem](https://lightmysky.com/learn/mathematics/sampling-distributions-and-the-central-limit-theorem-mt_nugaEeUSii) - [Conditional Probability from Tables and Venn Diagrams](https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP) ## Opens up - [Significance Tests for Chemical Data](https://lightmysky.com/learn/science/significance-tests-for-chemical-data-mt_2-SDgPjOQk) - [Beyond Accuracy: Precision, Recall and the Cost of an Error](https://lightmysky.com/learn/computing/beyond-accuracy-precision-recall-and-the-cost-of-an-error-mt_BHGgZM7tak) - [Hypothesis Tests for a Mean with the t-Distribution](https://lightmysky.com/learn/mathematics/hypothesis-tests-for-a-mean-with-the-t-distribution-mt_ig2o39hAwh) - [Testing a Binomial Proportion](https://lightmysky.com/learn/mathematics/testing-a-binomial-proportion-mt_ZJ8MTLYYKE)