Further Mathematics · Pearson Edexcel 9FM0 · Option FS1 · Topic 4

Hypothesis testing

Hypothesis tests for the mean of a Poisson distribution and the parameter of a geometric distribution, including critical regions.

2 sub-topics
1 in Year 12, 1 in Year 13
41 practice questions
2 animated lessons

Practice questions (41) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

4.1Hypothesis tests for the mean of a Poisson distributionY12
4.2Hypothesis tests for the parameter of a geometric distributionY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 41 questions in this topic, free, no account needed.

Hypothesis testing

Not needed for Year 12Easy

A tail probability for the geometric distribution · Year 13 · 1 mark

For $X \sim \mathrm{Geo}(p)$ , which gives $\mathrm{P}(X \geq x)$ ?
(1)

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$X \geq x$ means that the first $x - 1$ trials all fail.A: $(1 - p)^{x - 1}$

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Hypothesis testing

Not needed for Year 12Medium

A geometric tail probability · Year 13 · 1 mark

$X \sim \mathrm{Geo}(0.1)$ . What is $\mathrm{P}(X \geq 20)$ , to 3 decimal places?
(1)

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$\mathrm{P}(X \geq 20)$ ${}= (1 - 0.1)^{19}$ . $D$ : 0.135

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Hypothesis testing

Hard

Hypothesis test for a Poisson mean · Year 12 · 6 marks

The number of faults on a production line has historically followed a Poisson distribution with mean 1.2 per week. After a change of supplier, 10 faults are recorded in 5 weeks.

Test, at the 5% level of significance, whether the rate of faults has increased. State your hypotheses clearly.
(6)

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$\lambda$ is the mean for 5 weeks. $H_0: \lambda$ ${}= 6, \ H_1: \lambda > 6$
$X \sim \mathrm{Po}(6)$
$\mathrm{P}(X \geq 10) = 0.0839$
Compare with the significance level. $0.0839 > 0.05$
A conclusion in context.Do not reject H₀: there is insufficient evidence that the rate has increased.

Total6

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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