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Chi-Square Test · CAPE Applied Mathematics Unit 2

18 past-paper questions on Chi-Square Test, part of Module 2: Probability and Distributions, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

Practise Chi-Square Test
  1. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2State clearly the null and alternative hypotheses for a chi-square test to determine whether the number of employees who work overtime is independent of the distance of their home from the workplace.
  2. 4(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Find the expected frequencies if the null hypothesis is true.
  3. 4(b)(iii)9 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Using a 5% significance level, determine whether the number of employees who work overtime is independent of the distance of their home from the workplace. Clearly state your conclusion of the test.
  4. 4(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Determine the value of m and n shown in the table.
  5. 4(b)(ii)9 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Carry out a χ² goodness-of-fit test at the 5% significance level to determine whether the data may be modelled by a normal distribution with mean 9 and standard deviation 1.
  6. 3(c)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State appropriate null and alternative hypotheses to test for association between gender and rating of restroom facilities using a chi-squared test.
  7. 3(c)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the critical region for the chi-squared test at the 5% significance level.
  8. 3(c)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the expected frequency corresponding to cell (row 2, column 2), which has an observed value of 24.
  9. 3(c)(iv)a)1 mark· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State whether you reject or fail to reject the null hypothesis.
  10. 3(c)(iv)b)1 mark· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Interpret the test decision in the context of the problem.
  11. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State appropriate null and alternative hypotheses to test whether grades are uniformly distributed.
  12. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the critical region for the chi-squared goodness-of-fit test at the 5% significance level.
  13. 4(a)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the value of the chi-squared test statistic.
  14. 4(a)(iv)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State a valid conclusion for the test, giving a reason.
  15. 4(d)(i)1 mark· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Complete the table by giving the expected number of persons preferring each brand, assuming that each brand is equally likely to be preferred.
  16. 4(d)(ii)6 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Perform a \chi^2 goodness-of-fit test at the 1% significance level to determine whether a uniform distribution fits the tea-drinking preference of the 250 persons.
  17. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Complete the table to show the expected frequency for each day, assuming that haircuts are the same on each day.
  18. 4(b)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Carry out a goodness-of-fit analysis to test the hypothesis that the number of haircuts is the same for each day, using a 10% level of significance. Show full details of your method, and state your conclusion clearly.

Related topics in Module 2: Probability and Distributions