CAIE A-Level Mathematics A2 6.5.2 Normal Approximation Questions

Practise carrying out binomial hypothesis tests, finding rejection regions and interpreting significance levels.

Exam points

state hypotheses for a binomial model
find rejection regions and critical values at a significance level
draw justified conclusions from binomial test results

[Maximum number: 2]

At a certain large school it was found that the proportion of students not wearing correct uniform was 0.15 . The school sent a letter to parents asking them to ensure that their children wear the correct uniform. The school now wishes to test whether the proportion not wearing correct uniform has been reduced.

In fact 4 students out of the 50 are not wearing correct uniform.

State the conclusion of the test, explaining your answer.

$4 is outside critical region (\leqslant 3) OE or \mathrm{P}(X \leqslant 4)=0.112 which is >0.05 FT working from (c). No evidence that proportion not wearing the correct uniform has decreased (Accept Ho) In context not definite, e.g. not 'Proportion has not decreased'. No contradiction.$

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CAIE A-Level Mathematics A2 6.5.2 Normal Approximation Questions question 1