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Pearson Edexcel IAL Mathematics S3.4 Goodness of fit & contingency tables Question Bank

Practise chi-squared tests for distribution fit and independence, including hypotheses, expected frequencies, degrees of freedom and decisions.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • test whether a Poisson, binomial or uniform model fits observed frequency data
  • use contingency tables to test association between categories
  • choose degrees of freedom and a χ² critical value before making the conclusion

Covered syllabus points

S3.4.1 - null and alternative hypothesesS3.4.2 - Degrees of freedom

S3.4 - Goodness of fit and contingency tables question 1

[Maximum number: 12]

A research student is investigating the number of children who are girls in families with 4 children.

The table below shows her results for 200 such families.

Table for Question S3.4 - Goodness of fit and contingency tables question 1 — Edexcel A-Level Mathematics A2

The research student suggests that a binomial distribution with p=12p=\frac{1}{2} could be a suitable model for the number of children who are girls in a family of 4 children.

Question (a)

(a)

Using her results and a 5% significance level, test the research student's claim. You should state your hypotheses, expected frequencies, test statistic and the critical value used.

The research student decides to refine the model and retains the idea of using a binomial distribution but does not specify the probability that the child is a girl.

[ 8 ]

Question (b)

(b)

Test, at the 5% significance level, whether using a binomial distribution is suitable to model the number of children who are girls in a family of 4 children.
You should state your hypotheses and the critical value used.

[ 4 ]
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