5 mistakes learners make with hypothesis testing, each one named and explained.
Compare the probability of what you saw against the significance level, and never claim certainty.
The conclusion says the alternative hypothesis is accepted with certainty.
A clear result feels conclusive, and hedged wording sounds weaker than the evidence.
Question. A significant result at the 5 per cent level
A common answer. the coin is definitely biased
The answer. there is evidence that the coin is biased
Why. A 5 per cent test still leaves a real chance of a false positive.
Hypothesis tests never prove. Write evidence, sufficient evidence, or reject.
The region is written as greater than or equal when the alternative hypothesis was less than.
The inequality has to be copied from H1, and it is one symbol.
Question. H1: p < 0.4
A common answer. X >= 7
The answer. X <= 7
Why. A one-tailed test puts the region in the tail the alternative hypothesis points at.
Copy the direction straight from H1. They always match.
A value whose cumulative probability exceeds the significance level is included in the region.
The two cumulative probabilities straddle the level and choosing between them is the whole question.
Question. P(X <= 7) = 0.0301 and P(X <= 8) = 0.0611 at the 5 per cent level
A common answer. X <= 8
The answer. X <= 7
Why. 0.0611 is above 0.05, so including 8 would make the test more than 5 per cent.
Take the largest region whose probability is still below the level. Never the first one above it.
A probability below the significance level leads to not rejecting the null hypothesis.
Two small numbers and a comparison, with no intuition to say which way it should go.
Question. P(X >= 15) = 0.0207 at the 5 per cent level
A common answer. do not reject H0
The answer. reject H0
Why. 0.0207 is smaller than 0.05, so what was observed is unusually unlikely under H0.
Small probability means strong evidence. Small p, reject.
The conclusion talks about rejecting the alternative hypothesis.
Two hypotheses, and only the convention says which one is on trial.
Question. H0: p = 0.5, H1: p > 0.5, significant result
A common answer. reject H1
The answer. reject H0
Why. The null hypothesis is the one being tested; the alternative is never rejected.
Only H0 can be rejected. If your conclusion rejects H1, the hypotheses have swapped.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.