D.14 Answers: Numerical summaries for qualitative data
Answers to exercises in Sect. 14.9.
Answer to Exercise 14.1:
1. Vomited: 0.50 had beer then wine; 0.50 had wine only.
Didn’t vomit: 0.738 had beer then wine, 0.262 had wine only. They tell us the proportion that drank various things, among those who did and didn’t vomit. 2. Beer then wine: 8.8% vomited and 91.2% didn’t; Wine only: 21.4% vomited and 78.6% didn’t. They tell us the percentage that vomited, for each drinking type. 3. \((6 + 6)/(6 + 6 + 62 + 22) = 0.125\). 4. \(6/22 = 0.2727\). 5. \(6/62 = 0.096774\). 6. \(0.27272/0.096774 = 2.82\). 7. \(0.096774/0.27272 = 0.354\).
Didn’t vomit: 0.738 had beer then wine, 0.262 had wine only. They tell us the proportion that drank various things, among those who did and didn’t vomit. 2. Beer then wine: 8.8% vomited and 91.2% didn’t; Wine only: 21.4% vomited and 78.6% didn’t. They tell us the percentage that vomited, for each drinking type. 3. \((6 + 6)/(6 + 6 + 62 + 22) = 0.125\). 4. \(6/22 = 0.2727\). 5. \(6/62 = 0.096774\). 6. \(0.27272/0.096774 = 2.82\). 7. \(0.096774/0.27272 = 0.354\).
Answer to Exercise 14.2:
1. \(91/(91 + 188) = 0.32616\).
2. \(188/91 = 2.0659\), or about 2.07.
3. \(22/13 = 1.6923\), or about 1.69.
4. \(13/(13 + 22) = 0.37142\), or about 37.1%.
5. \(2.0659/1.6923 = 1.22\).
Answer to Exercise 14.3:
1. 21/114, or about 18.4%.
2. 14/54, or about 25.9%.
3. 7/60, or about 11.7%.
4. 21/93, or about 0.226.
5. 14/40, or 0.35.
6. 7/53, or about 0.132.
7. 0.35/0.132, or about 2.7.
8. The odds of no August rainfall in Emerald is 2.7 times higher in months with non-positive SOI.
Answer to Exercise 14.4:
1. 45.9%.
2. 61.4%.
3. 0.848.
4. 1.59.
5. 1.15.
6. 0.533.
7. The odds of reporting back pain from carrying school bags,
comparing boys to girls.