Quelpr

Chi-Square Test · CAPE Applied Mathematics Unit 1

60 past-paper questions on Chi-Square Test, part of Module 3: Analysing and Interpreting Data, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise Chi-Square Test
  1. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2State appropriate null and alternative hypotheses.
  2. 6(a)(ii)11 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2On the answer sheet provided, complete the table where O denotes the observed frequency, E denotes the expected frequency and N denotes the total frequency, 400, when the null hypothesis is true.
  3. 6(a)(iii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Determine the number of degrees of freedom for this hypothesis test.
  4. 6(a)(iii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Determine the critical region for this hypothesis test.
  5. 6(a)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Clearly state the conclusion that may be drawn from this test.
  6. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2State clearly the null and alternative hypotheses.
  7. 6(a)(ii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Calculate, to the nearest whole number, the expected number of textbooks with hard back covers.
  8. 6(a)(ii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Calculate, to the nearest whole number, the expected number of novels with paper back covers.
  9. 6(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Identify the rejection region for this test.
  10. 6(a)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2The calculated χ² value is 9.2649. State clearly the conclusion of this test.
  11. 6(b)3 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Given that the critical value for χ² is 9.488, use your tables to determine the degrees of freedom and the significance level.
  12. 6(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Formulate null and alternate hypotheses for this test.
  13. 6(c)(ii)5 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the expected frequencies, E, when the null hypothesis is true.
  14. 6(c)(iii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Determine the number of degrees of freedom.
  15. 6(c)(iii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Determine the critical region.
  16. 6(c)(iii)c)5 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the test statistic.
  17. 6(c)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2State clearly, with reason, your conclusion of the test.
  18. 6(a)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Determine the number of degrees of freedom for the test.
  19. 6(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Determine the critical region for the test.
  20. 6(a)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Copy and complete the table showing the expected frequencies for EACH cell.
  21. 6(a)(v)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2The calculated χ² test value is 9.534. Clearly state the conclusion that can be drawn from this test.
  22. 6(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2State appropriate null and alternative hypotheses for this test.
  23. 6(b)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Copy and complete the table of observed (O) and expected (E) frequencies of the grades obtained in the examination.
  24. 6(b)(iii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Determine the number of degrees of freedom for this hypothesis test.
  25. 6(b)(iii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Determine the critical region of the test.
  26. 6(b)(iii)c)5 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Calculate the χ² test statistic.
  27. 6(b)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Clearly state the conclusion which may be drawn from this test.
  28. Q321 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1For a contingency table with 4 rows and 3 columns, the number of degrees of freedom for a \chi^2 test of independence is
  29. Q361 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1If X is a \chi^2 distribution with 12 degrees of freedom, then the value of P(X < 4.404) is
  30. Q431 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1A chi-squared test does NOT
  31. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2State the null and alternative hypotheses for this test.
  32. 6(a)(ii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Determine the number of degrees of freedom for the test.
  33. 6(a)(ii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Determine the critical region for the test.
  34. 6(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Determine the expected frequency for the cell in the third row and second column (observed count 15).
  35. 6(a)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2The calculated chi-square test statistic is 9.1625. State the conclusion of the test.
  36. Q311 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1In a chi-squared test for independence between the variables X and Y, the number of degrees of freedom is
  37. Q321 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1The expected value of the cell which contains the number 15, (Y_2, X_1), to the NEAREST whole number is
  38. 6(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2State appropriate null and alternate hypotheses for this chi-squared test.
  39. 6(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Determine the critical value of the test at the 5% level of significance.
  40. 6(c)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate the expected number of students who attended School B and received a Grade II.
  41. 6(c)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Given the calculated chi-squared test value is 9.1625, clearly state the conclusion that may be drawn.
  42. Q401 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1Items 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The number of degrees of freedom is
  43. Q411 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1Items 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The critical value at the 5% significance level appropriate to this…
  44. Q421 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1Item 42 refers to the following contingency table which gives the results of a football team over 40 matches. \begin{tabular}{|l|c|c|c|} \hline & \textbf{Good Weather} & \textbf{Bad Weather} & \textbf{Total} \\ \hline…
  45. Q311 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1Items 31--32 refer to the following contingency table which shows the observed results used to investigate whether the variables X and Y are independent. \begin{tabular}{|c|c|c|c|} \hline & X_1 & X_2 & X_3 \\…
  46. Q321 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1Items 31--32 refer to the following contingency table which shows the observed results used to investigate whether the variables X and Y are independent. \begin{tabular}{|c|c|c|c|} \hline & X_1 & X_2 & X_3 \\…
  47. Q381 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The parameter of a \chi^2 distribution is the
  48. Q391 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The grades given by 3 teachers at a school are displayed in a 3 \times 5 contingency table. A \chi^2 test, at the 5\% level of significance, is carried out to test the hypothesis that there is no association…
  49. 6(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2State clearly the null and alternative hypotheses.
  50. 6(b)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Calculate, to the nearest whole number, the expected number of males that have no opinion.
  51. 6(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Identify the rejection region of the test.
  52. 6(b)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2The calculated chi-square value of the test is 9.8249. State clearly the conclusion for this test, giving a reason for your answer.
  53. Q401 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1Items 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The number of degrees of freedom is
  54. Q411 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1Items 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The critical value at the 5% significance level appropriate to this…
  55. Q421 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1Item 42 refers to the following contingency table which gives the results of a football team over 40 matches. A \chi^2 test of independence is conducted to determine if the weather has an effect on the result of the…
  56. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Formulate the null and alternative hypotheses for the chi-square test.
  57. 6(a)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Complete the table to show the missing expected frequencies and marginal totals.
  58. 6(a)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Calculate the chi-square test statistic value.
  59. 6(a)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the critical region of the test at the 5% level of significance.
  60. 6(a)(v)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2State clearly the conclusion that may be drawn from this test.

Related topics in Module 3: Analysing and Interpreting Data