Pearson Edexcel IAL Mathematics S2.4.6 Hypothesis tests for the parameter p

Practise binomial and Poisson hypothesis tests by forming hypotheses, finding critical regions, and judging significance from sample data.

Exam points

test a binomial proportion p using B(n,p), tail probabilities and a stated conclusion
find two-tailed critical regions with rejection probabilities close to the target level
use a Poisson or Normal approximation test for rates, including continuity correction when needed

[Maximum number: 5]

In a peat bog, Common Spotted-orchids occur at a mean rate of 4.5 per $\mathrm{m}^{2}$

Juan believes that by introducing a new management scheme the number of Common Spotted-orchids in the peat bog will increase. After three years under the new management scheme, a randomly selected 2 m^2 of the peat bog contains 11 Common Spotted-orchids.

Using a 5% significance level assess Juan's belief. State your hypotheses clearly.

$\mathrm{H}_{0}: \lambda=9 \mathrm{H}_{1}: \lambda>9$

B1

$M \sim \operatorname{Po}(9) \quad \mathrm{P}(M \geq 11)=1-\mathrm{P}(M \leq 10) \quad$ or $\mathrm{P}(M \geq 15)=0.0415$

M1

=0.294 or CR $M \geq 15$

A1

Accept $\mathrm{H}_{0}$ or insignificant or 11 does not lie in the critical region

dM1

There is insufficient evidence to support Juan's belief

A1

(5)

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S2.4.6 - Hypothesis tests for the parameter p question 1