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Hypothesis Testing · CAPE Applied Mathematics Unit 1

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

Practise Hypothesis Testing
  1. 5(b)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Using symbols only, state appropriate null and alternative hypotheses.
  2. 5(b)(iii)4 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2State the critical region(s) for this test.
  3. 5(b)(iv)6 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Using an appropriate continuity correction, calculate the test statistic.
  4. 5(b)(v)3 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Supporting your answer with a reasoned argument, state the conclusion that may be drawn from the hypothesis test.
  5. 5(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2State in symbols the null and alternative hypotheses for testing if the dice yield fewer 9s than expected.
  6. 5(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Determine the critical region for this hypothesis test at the 5% significance level.
  7. 5(b)(iv)5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Calculate the appropriate test statistic.
  8. 5(b)(v)1 mark· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Clearly state the conclusion drawn from the test.
  9. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2State appropriate null and alternative hypotheses for this test.
  10. 5(c)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Formulate suitable null and alternative hypotheses (using statistical symbols) to test whether the mean amount of coffee dispensed is 10 ounces or whether it is less than 10 ounces.
  11. Q311 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1In a one-tailed hypothesis test, the critical value divides the total region under a sampling distribution into
  12. Q401 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The mean age of teachers in a certain country is 30 years. A random sample of 49 teachers yields a mean age of 33.08 years. Using a population standard deviation of 12 years, a z-test at the 5\% significance level…
  13. Q441 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1A balloon manufacturing company claims that at least 10\% of its balloons are blue. A random sample of 200 of these balloons is taken, and 16 are found to be blue. Which of the following tests would be MOST…
  14. Q341 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1In a hypothesis test for a population proportion p, the null hypothesis is p = 0.64 and the alternative hypothesis is p \neq 0.64. A sample of 400 elements from the population produced a sample proportion of 0.58.…
  15. Q351 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1A balloon manufacturing company claims that at least 10% of its balloons are blue. A random sample of 200 of these balloons is taken, and 16 are found to be blue. Which of the following tests would be MOST appropriate…
  16. Q361 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1In a one-tailed z-test, the null hypothesis H_0 : \mu = 30 is tested against the alternative hypothesis H_1 : \mu > 30. At the 10% significance level, the critical z region is
  17. Q431 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1In hypotheses testing, the probability of committing a type-I error is called the
  18. 5(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2State null and alternative hypotheses, using statistical symbols to test whether the mean mass has changed.
  19. 5(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Determine the critical region(s) of the test conducted at the 4% significance level.
  20. 5(c)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate the value of the test statistic used in this test.
  21. 5(c)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Clearly state the conclusion of the test.
  22. Q311 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1In a hypothesis test at the 5% level of significance, the null hypothesis is
  23. Q331 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1In a one-tailed z-test, the null hypothesis H_0: \mu = 12 is tested against the alternative hypothesis H_1: \mu > 12. At the 5% significance level, the critical z region is
  24. Q441 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1A balloon manufacturing company claims that 10% of its balloons are blue. A random sample of 200 of these balloons is taken, and 16 are found to be blue. Which of the following tests would be MOST appropriate for…
  25. 5(c)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2State, in symbols, appropriate null and alternative hypotheses for the test.
  26. Q331 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1In a one-tailed z-test, the null hypothesis H_0 : \mu = 12 is tested against the alternative hypothesis H_1 : \mu > 12. At the 5\% significance level, the critical z region is
  27. Q431 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1In hypotheses testing, the probability of committing a Type I error is called the
  28. 6(a)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2State clearly the null and alternate hypotheses.
  29. 6(a)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Identify the critical region(s) of the test statistic.
  30. 6(a)(iii)4 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Calculate the value of the test statistic.
  31. 6(a)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2State clearly a valid conclusion of the test, giving a reason for your answer.
  32. Q331 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1The mean age of teachers in a certain country is 30 years. A random sample of 49 teachers yields a mean age of 33.08 years. Using a population standard deviation of 12 years, a z-test at the 5% significance level was…
  33. Q371 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1A balloon manufacturing company claims that at least 10% of its balloons are blue. A random sample of 200 of these balloons is taken, and 16 are found to be blue. Which of the following tests would be MOST appropriate…
  34. 5(a)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Formulate the null and alternative hypotheses.
  35. 5(a)(v)1 mark· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the critical value for the test.
  36. 5(a)(vi)1 mark· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the rejection region.
  37. 5(a)(vii)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Given that the test statistic is -1.59, state clearly a valid conclusion for the test.
  38. 5(a)(vi)a4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Test the null hypothesis H_0 : p = 0.40 against the alternative H_1 : p > 0.40 at the significance level of alpha = 0.05: Calculate the test statistics.
  39. 5(a)(vi)b1 mark· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Determine the critical value.
  40. 5(a)(vi)c1 mark· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Determine the critical region.
  41. 5(a)(vi)d2 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2State a valid conclusion for the test. Give ONE reason for the conclusion stated.

Related topics in Module 3: Analysing and Interpreting Data