Loading [MathJax]/jax/element/mml/optable/Latin1Supplement.js

User interface language: English | Español

Date May Example question Marks available 8 Reference code EXM.1.AHL.TZ0.55
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Test and Calculate Question number 55 Adapted from N/A

Question

Eggs at a farm are sold in boxes of six. Each egg is either brown or white. The owner believes that the number of brown eggs in a box can be modelled by a binomial distribution. He examines 100 boxes and obtains the following data.

Calculate the mean number of brown eggs in a box.

[1]
a.i.

Hence estimate p, the probability that a randomly chosen egg is brown.

[1]
a.ii.

By calculating an appropriate χ2 statistic, test, at the 5% significance level, whether or not the binomial distribution gives a good fit to these data.

[8]
b.

Markscheme

Note: Candidates may obtain slightly different numerical answers depending on the calculator and approach used. Use discretion in marking.

Mean =1×29++6×1100=1.98       (A1)

[1 mark]

a.i.

Note: Candidates may obtain slightly different numerical answers depending on the calculator and approach used. Use discretion in marking.

ˆp=1.986=0.33      (A1)

[1 mark]

a.ii.

Note: Candidates may obtain slightly different numerical answers depending on the calculator and approach used. Use discretion in marking.

The calculated values are

f0               fe        (f0fe)2
10            9.046         0.910
29          26.732          5.14       (M1)
31          32.917         3.675      (A1)
18          21.617       13.083      (A1)
12            9.688         5.345      (A1)

Note: Award (M1) for the attempt to calculate expected values, (A1) for correct expected values, (A1) for correct (f0fe)2 values, (A1) for combining cells.

χ2=0.9109.046++5.3459.688=1.56      (A1)

OR

χ2=1.56      (G5)

Degrees of freedom = 3; Critical value = 7.815

(or p-value = 0.668 (or 0.669))      (A1)(A1)

We conclude that the binomial distribution does provide a good fit.      (R1)

[8 marks]

b.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.8—Binomial distribution
Show 139 related questions
Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
Topic 4—Statistics and probability » AHL 4.12—Data collection, reliability and validity tests
Topic 4—Statistics and probability

View options