A.10 Answer: TW 10 tutorial

Answers for Sect. 10.2

If the RQ is about odds (and hence odds ratios), then the hypothesis, CI and hypothesis tests should also be about odds.

(Similarly, if the RQ is about proportions, then the hypothesis, CI and hypothesis tests should also be about proportions.)

Answers for Sect. 10.3

  1. See Table A.2.
  2. Side-by-side or stacked bar chart.
  3. \(352/2512 = 0.1401\).
  4. \(336/2328 = 0.1443\).
  5. \(0.1401/0.1443 = 0.971\).
  6. The odds ratio, of a boy maturing late compared to a girl maturing late.
  7. OR: \(0.971\), with \(95\)% CI from \(0.828\) to \(1.139\).
  8. See Table A.3.
  9. \(P = 0.717\); no evidence of a difference between boys and girls.
TABLE A.2: Maturation data table.
Late Not late Total
Males 352 2512 2864
Females 336 2328 2664
Total 688 4840 5528
TABLE A.3: Nunmerical summary table for maturation data.
Prop late Odds late Sample size
Males 0.123 0.1401 2864
Females 0.126 0.1443 2664
Diff: -0.003 OR: 0.971

Answers for Sect. 10.4

Some answers embedded.

  1. See Table A.4.

  2. Use of artificial limb is the explanatory variable.

  3. Using artificial limb: \(49/16 = 3.0625\). Not using artificial limb: \(21/19 = 1.105263\). The OR is \(3.0625/1.105263 = 2.771\); that is, the odds of being alive after five years is almost three times higher for those using an artificial limb compared to those who do not. See Table A.5.

  4. The CI for the OR is from \(1.198\) to \(6.411\).

  5. Chi-squared: \(5.836\); like \(z = \sqrt{5.836/1} = 2.42\): large; \(P\) about \(0.016\).

    The sample provides evidence to suggest that the odds of dying within five years is not the same between having a wearing an artificial limb and the five-year mortality rate in the population (\(\text{chi-square} = 5.836\); \(\text{df} = 1\); \(P = 0.016\); OR: \(2.771\) and \(95\)% CI from \(1.198\) to \(6.411\)).

TABLE A.4: Five-year mortality for artifical limb users.
Alive Dead Total
Used art. limb 49 16 65
Did not use art. limb 21 19 40
Total 70 35 105
TABLE A.5: Five-year mortality and use of an artificial limb: Numerical summary.
Percentage alive after 5 years Odds alive after 5 years Sample size
Use artificial limb 75.4 3.06 65
Did not use artifical limb 52.5 1.11 40
Diff in percentages: 22.9 OR: 2.771 626

Answers for Sect. 10.5

1. Two-sample \(t\)-test. 2. A \(\chi^2\) test. 3. A paired \(t\)-test. 4. A two-sample \(t\)-test. 5. A \(z\)-test comparing two proportions. 6. None of the other options are correct: requires regression or correlation.

Answers for Sect. 10.6

\(n = (2\times 7.145\div 0.5)^2 = 816.8\), so use guesses from \(817\) students.

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