Chi squared tests questions

Questions to attempt

3 questions on Chi squared tests, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FS1-6.1 · Goodness of fit tests and contingency tables. The null and alternative hypotheses. Degrees of freedom.

   Q1

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   1.

   After fitting a one-parameter model from the same data, five ordered categories have observed frequencies $41,33,17,7,2$ and expected frequencies $40,32,18,7,3$. Carry out a goodness-of-fit test at the $5\%$ level of significance. The critical value for $2$ degrees of freedom is $5.991$.

   (8)

   (Total for Question 1 is 8 marks)

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2. FS1-6.1 · Goodness of fit tests and contingency tables. The null and alternative hypotheses. Degrees of freedom.

   Q2

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   2.

   A goodness-of-fit test has four categories with model probabilities $0.1,0.2,0.3,0.4$ and a sample size of $120$. No parameter is estimated. Find the expected frequencies and the degrees of freedom.

   (3)

   (Total for Question 2 is 3 marks)

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3. FS1-6.1 · Goodness of fit tests and contingency tables. The null and alternative hypotheses. Degrees of freedom.

   Q3

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   3.

   The observed counts for travel method by year group are $\begin{array}{c|rrrr}&\text{walk}&\text{cycle}&\text{bus}&\text{car}\\ \hline \text{Year 10}&24&18&20&18\\ \text{Year 11}&16&22&20&22\\ \text{Year 12}&10&20&30&20\end{array}$. Test independence at the $5\%$ level of significance. The critical value for $6$ degrees of freedom is $12.592$.

   (10)

   (Total for Question 3 is 10 marks)

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FS1-6 Chi squared tests revision notes