HYPOTHESIS TESTING USING THE BINOMIAL DISTRIBUTION The Problem Solving Approach

Aims of the lesson 1. To show the point of Hypothesis testing 2. To encourage discussion 3. Emphasize worded conclusions Reject H 0

Aim when using PSA Conduct an experiment VS Work through a mathematical exercise. ‘We started with 3 unlabelled cups of coke...’ H o : p = 1/3 H 1 : p > 1/3 n = 11 sig. = 5% X ~ B(11, 1/3) P(X ≥ 6) = 1 – P(X ≤ 5) = P(X ≥ 7) = 1 – P(X ≤ 6) = Critical region is x ≥ 7 x = 10 so reject H 0

Lesson Plan 1. Collect 2. Discuss aims and plan 3. Find critical regions 4. Reveal results and discuss conclusion

Collect CorrectIncorrect

Discuss Aims and plan Q: Is it possible to taste the difference between Tesco’s coke and the ‘Real Thing’?

Find Critical Regions

Reveal results and discuss conclusion ‘We have enough evidence to accept the claim that there is a difference in taste between Coca Cola and Tesco’s own brand cola.’

What went well Students all had an opinion so were engaged Something for everyone to take part in Everyone could understand the point of the test Results not revealed until the end

To Try Next Time Students were cola enthusiasts so difference was clear – they were not really interested in the conclusion of the test. Next time: Ask the students for something they would like to test. Try to ensure result will not be obvious.

To Try Next Time Different significance levels made the conclusion seem arbitrary. Next time: Have some examples to show in which situations you would use which significance level.

Using the PSA at different stages Class 1Class 2 TablesEXPERIMENT Finding regions Practice like P(X≥8) Finding Hypotheses 1 tailed tests EXPERIMENT Practice

Using the PSA at different stages Class 1Class 2 Strong technicallyGood conclusions Conclusions somewhat Some short cuts with an afterthoughttheory HENCE: PSA more effective when used from the start?

Using the PSA at different stages Mathematical Statistical harder than Statistical Mathematical

Summary Good as an introduction to a topic Increases motivation Encourages discussion Shows what ‘the point’ of all the maths is Improve on discussion of significance levels