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Edexcel A-Level Mathematics A2 S3.4.1 Null and Alternative Hypotheses Questions

Practise chi-squared null and alternative hypotheses for goodness-of-fit and independence tests, linking them to observed and expected frequencies with Edexcel IAL mark-scheme evidence.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • state H0 and H1 for whether a named distribution is a suitable model
  • distinguish independence from association when writing hypotheses for a contingency table
  • link hypotheses to observed and expected frequencies in a χ² test

Edexcel A-Level Mathematics A2 S3.4.1 Null and Alternative Hypotheses Questions question 1

[Maximum number: 8]

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 Edexcel A-Level Mathematics A2 S3.4.1 Null and Alternative Hypotheses Questions 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.

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.

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