Statistics · Hypothesis testing
Chapter 1 · 4
The idea
Setting up a hypothesis test
The language and structure of a binomial hypothesis test: the population proportion p, the null hypothesis H0 : p = p0 and the alternative hypothesis H1, deciding between a one-tailed (p < p0 or p > p0) and a two-tailed (p ≠ p0) test from the wording, the test statistic X ~ B(n, p0) under H0, and what the significance level means.
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Statistics · Hypothesis testing
Setting up a hypothesis test
The language and structure of a binomial hypothesis test: the population proportion p, the null hypothesis H0 : p = p0 and the alternative hypothesis H1, deciding between a one-tailed (p < p0 or p > p0) and a two-tailed (p ≠ p0) test from the wording, the test statistic X ~ B(n, p0) under H0, and what the significance level means.
Why it works
Reasoning from surprise
A hypothesis test uses the result of one sample to decide between two competing claims about a population parameter — here a population proportion (the probability of "success": a defective item, a red bead, a late customer). We can't see the whole population, so we reason from how surprising the sample would be if a particular value of were true.The two hypotheses
The null hypothesis is the "no change / status quo" claim, and is always an equality: . The alternative is what you are testing for, and its form is chosen from the wording:Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
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