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/√176=0.2728678 days; echinacea group 3.31/√183=0.2446822 days. 2. 0.53±(2×0.367), 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±(2×0.2446822), 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/√10=0.4427189;
splinting group: 1.1/√10=0.3478505.
2. Splinting minus exercise:
the difference are how much greater the pain is with splinting.
3. 0.3±(2×0.563, or from -0.826 to 1.426:
0.826 greater pain with exercise to 1.426 greater pain with splinting.
4. 1.1±(2×0.3478505): from 0.404 to 1.796.
5. Sample sizes are small; CIs may not be statistically valid,
roughly correct only.