CAIE A-Level Mathematics 6.5.2 Binomial and Poisson Hypothesis Tests

Practise testing a proportion or event rate from one observation using exact binomial or Poisson probabilities, or a justified normal approximation with continuity correction.

Exam points

state H₀ and H₁ for p or λ and select the lower, upper or two-tailed event
calculate the observed tail directly from B(n, p) or Po(λ), including all equally extreme values
when justified, use the matching normal mean and variance with continuity correction before testing

[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.

$4 is outside critical region (\leqslant 3) OE or \mathrm{P}(X \leqslant 4)=0.112 which is >0.05 M1 FT working from (c). No evidence that proportion not wearing the correct uniform has decreased (Accept Ho) A1 In context not definite, e.g. not 'Proportion has not decreased'. No contradiction.$

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6.5.2—Normal approximation question 1