Pearson Edexcel IAL Mathematics S3.4.1 null & alternative hypotheses

Practise writing null and alternative hypotheses for chi-squared tests on fitted distributions and contingency-table independence.

Exam points

state H_0 and H_1 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

[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 S3.4.1 - null and alternative hypotheses question 1 — Edexcel A-Level Mathematics A2

The research student suggests that a binomial distribution with $p=\frac{1}{2}$ 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.

$H_0$ : B(4,0.5) is a suitable model.
$H_1$ : B(4,0.5) is not a suitable model.
B1
Expected frequencies: 12.5, 50, 75, 50, 12.5.
M1 A1
$\sum \frac{(O-E)^2}{E}=\frac{(15-12.5)^2}{12.5}+\cdots+\frac{(10-12.5)^2}{12.5}$
or
$\sum \frac{O^2}{E}-N=\frac{15^2}{12.5}+\cdots+\frac{10^2}{12.5}-200$
A1
v=4
B1
$\chi^2_4(0.05)=9.488$ , critical region >9.488.
B1
Sufficient evidence to say that the research student's claim is not supported.
A1 ft
M1 M1

Figure for Answer to Question S3.4.1 - null and alternative hypotheses question 1 — Edexcel A-Level Mathematics A2

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S3.4.1 - null and alternative hypotheses question 1