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t-test · CAPE Applied Mathematics Unit 1

37 past-paper questions on t-test, part of Module 3: Analysing and Interpreting Data, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise t-test
  1. 5(a)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2For testing H0: mu = 45 versus H1: mu < 45 at the 5% significance level, determine the critical region.
  2. 5(a)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Calculate the value of the test statistic for this hypothesis test.
  3. 5(a)(ii)c)1 mark· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Clearly state the conclusion of the test.
  4. 6(b)(i)1 mark· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2State the assumption that must be made under which a t-test is valid.
  5. 6(b)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2State clearly the null and alternative hypotheses for the test.
  6. 6(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Identify the critical region for this test.
  7. 6(b)(iv)5 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Calculate the test statistic to be used in this test.
  8. 6(b)(v)3 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2State clearly the conclusion for this test, giving a reason for your answer.
  9. 5(c)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2State TWO conditions that are necessary for the valid use of a t-test to test a hypothesis about the mean of X.
  10. 5(c)(iii)8 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Assuming a t-test is valid, test at the 5% significance level whether the advertisement was overstating the battery life. Clearly state: a) null and alternative hypotheses, b) test value, c) critical region, d)…
  11. 5(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2State TWO conditions why a t-test will be appropriate to test the hypothesis that the machine is not dispensing on average 10 ounces of coffee.
  12. 5(c)(iii)7 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Test at the 5% level of significance whether the machine is dispensing on average 10 ounces of coffee.
  13. Q351 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1A t-test is used to test a company's claims that its watch batteries last an average of 7 years. A sample of 10 of the company's watch batteries has a mean life of 6.75 years and a standard deviation of 0.5 years. The…
  14. Q391 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The cholesterol levels of 8 women are \begin{array}{cccc} 3.1 & 2.7 & 1.3 & 1.4 \\ 1.7 & 3.3 & 2.4 & 1.9 \end{array} In conducting a t-test on the mean, the number of degrees of freedom is
  15. 5(a)(ii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2State in statistical symbols the null and alternative hypotheses.
  16. 5(a)(ii)b)4 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Determine the critical region for the test.
  17. 5(a)(ii)c)3 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Calculate the value of the test statistic.
  18. 5(a)(ii)d)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Clearly state the conclusion of this hypothesis test.
  19. 5(a)(ii)e)1 mark· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2State the assumption required to perform this test.
  20. Q341 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1The t-test statistic is used to test the population mean when the variable X is
  21. Q351 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1A t-test is used to test whether solar coils last an average of 7 years. A sample of 10 of these solar coils have a mean life of 6.75 years and a standard deviation of 0.5 years. The value of the test statistic, t,…
  22. Q361 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1The cholesterol levels of 5 women are \begin{tabular}{ccccc} 3.1 & 2.7 & 3.3 & 2.4 & 1.9 \\ \end{tabular} When conducting a t-test on the mean at the 5% level of significance using a one-tailed test, the critical…
  23. Q391 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1The cholesterol levels of 8 women are \begin{tabular}{cccc} 3.1 & 2.7 & 1.3 & 1.4 \\ 1.7 & 3.3 & 2.4 & 1.9 \\ \end{tabular} In conducting a t-test on the mean, the number of degrees of freedom is
  24. 5(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Determine the critical region(s) for the test.
  25. 5(c)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Calculate the value of the test statistic.
  26. 5(c)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2State your conclusions, giving reasons.
  27. Q341 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The t-test statistic is used to test the population mean when the variable X is
  28. Q321 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1The value of t for 16 degrees of freedom and a P(T \le t) = 0.90 is
  29. Q341 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1The t-test statistic is used to test the population mean when the variable X is
  30. Q351 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1A t-test is used to test whether solar coils last an average of 7 years. A sample of 10 of these solar coils have a mean life of 6.75 years and a standard deviation of 0.5 years. The value of the test statistic, t,…
  31. Q441 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1When using a small sample of size, n, to construct a confidence interval for the population mean, the number of degrees of freedom for the t-distribution is
  32. 5(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Identify the distribution that can be used to model this situation, giving ONE reason.
  33. 5(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the critical value.
  34. 5(b)(iii)1 mark· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the rejection region.
  35. 5(b)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Given that the mean is 30.5 and the standard deviation is 10.6, calculate the test statistic.
  36. 5(b)(v)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2State clearly a valid conclusion for the test.
  37. 6(c)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the critical region for a test of H0: mu = 14.0 against H1: mu != 14.0 at the 5% significance level.

Related topics in Module 3: Analysing and Interpreting Data