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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Write H0 with equals about the population, pick the tail from the claim, and fix alpha before the data arrive.
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.