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Date May Example question Marks available 14 Reference code EXM.1.AHL.TZ0.56
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Test and State Question number 56 Adapted from N/A

Question

A zoologist believes that the number of eggs laid in the Spring by female birds of a certain breed follows a Poisson law. She observes 100 birds during this period and she produces the following table.

The zoologist wishes to determine whether or not a Poisson law provides a suitable model.

Calculate the mean number of eggs laid by these birds.

[2]
a.

Write down appropriate hypotheses.

[2]
b.i.

Carry out a test at the 1% significance level, and state your conclusion.

[14]
b.ii.

Markscheme

Mean  = 1 × 19 + 2 × 34 + + 5 × 4 100        (M1)

= 2.16          A1  N2

[2 marks]

a.

H0 : Poisson law provides a suitable model          A1

H1 : Poisson law does not provide a suitable model          A1

[2 marks]

b.i.

The expected frequencies are

        A1A1A1A1A1A1

Note: Accept expected frequencies rounded to a minimum of three significant figures.

χ 2 = ( 10 11.533 ) 2 11.533 + + ( 4 6.824 ) 2 6.824           (M1)(A2)

= 5.35    (accept 5.33 and 5.34)       A2

v = 4    (6 cells − 2 restrictions)          A1

Note: If candidates have combined rows allow FT on their value of v .

Critical value  χ 2 = 13.277

Because 5.35 < 13.277, the Poisson law does provide a suitable model.          R1  N0

[14 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
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Topic 4—Statistics and probability » AHL 4.12—Data collection, reliability and validity tests
Topic 4—Statistics and probability » AHL 4.17—Poisson distribution
Topic 4—Statistics and probability

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