D.23 Answers: CIs for two means
Answers to exercises in Sect. 24.13.
Answer to Exercise 24.1:
1. Table D.3.
2. From SPSS, exact 95% CI: 0.05438 to 0.11501 (bottom row).
Exact 95% CI for the difference between the mean direct HDL cholesterol concentrations:
0.05438 to 0.11501 mm Hg higher for non-smokers.
| Mean | Standard deviation | Standard error | Sample size | |
|---|---|---|---|---|
| Non-smokers | 1.3924 | 0.42792 | 0.01048 | 1668 |
| Smokers | 1.3077 | 0.42353 | 0.01137 | 1388 |
| Differences | 0.0847 | 0.01546 |
Answer to Exercise 24.2: 1. Placebo group: \(3.62/\sqrt{176} = 0.2728678\) days; echinacea group \(3.31/\sqrt{183} = 0.2446822\) days. 2. \(0.53 \pm (2\times 0.367)\), or -0.204 to 1.264 days. 3. Placebo minus echinacea: the difference between the means show how much longer symptoms last with placebo, compared to echinacea. 4. \(6.34 \pm (2\times 0.2446822)\), or 5.85 to 6.83 days. 5. Sample sizes are large, so the CIs statistically valid.
The difference between the means is an average of 0.53 days; about half a day (quicker on echinacea). Probably not that important when a cold last for almost seven days.
Answer to Exercise 24.3:
1. Exercise group: \(1.4/\sqrt{10} = 0.4427189\);
splinting group: \(1.1/\sqrt{10} = 0.3478505\).
2. Splinting minus exercise:
the difference are how much greater the pain is with splinting.
3. \(0.3\pm (2\times 0.563\), or from -0.826 to 1.426:
0.826 greater pain with exercise to 1.426 greater pain with splinting.
4. \(1.1\pm (2\times 0.3478505)\): from 0.404 to 1.796.
5. Sample sizes are small; CIs may not be statistically valid,
roughly correct only.