# Seminar aus Statistik für das Magisterstudium - Example 5.5

From StatWiki

(From Day (1988)): In a study of nausea after anaesthesia the expected rates are TLS= 0.10, it,= 0.20, and we want a power of 80% to detect this difference at the 1% level.

- How many patients are required?

```
> power.prop.test(p1=0.1,p2=0.2,power=0.8,sig.level=.01)
Two-sample comparison of proportions power calculation
n = 296.3702
p1 = 0.1
p2 = 0.2
sig.level = 0.01
power = 0.8
alternative = two.sided
NOTE: n is number in *each* group
```

- If that difference were observed, what would the 95 confidence limits be?

```
> sqrt(4 * qnorm(1-(.05/2))^2 * (0.1 * (1 - 0.1) + 0.2 * (1-0.2)) / 297) # gesamte breite
[1] 0.1137286
```

- If an accuracy of —2% to +2% were required for the estimate of the difference, what sample size would be required?
- Suppose the observed difference were smaller, with rates of 10% versus 12%; what would the confidence interval be?
- To obtain limits within —2% and +2%, how large should the sample be?