The simulation results for the 20 hypothetical patients are as follows:
- First 5 patients: 2 cures
- First 10 patients: 3 cures
- All 20 patients: 7 cures
Now, we can proceed to calculate the confidence intervals for each group using an online tool like GraphPad or a similar statistical method to determine the 90%, 95%, and 99% confidence intervals.
Reflection:
Random Determination: Each patient had a 50% chance of being "cured" or "not cured" using a random number generator.
Confidence Intervals:
- Calculating confidence intervals at 90%, 95%, and 99% levels for each group (first 5, first 10, and all 20 patients) will help to estimate the range in which the true cure rate is likely to fall for each sample size.
Interpretation of Confidence Intervals: The confidence interval lengths vary depending on the sample size and the confidence level. Larger samples generally yield narrower confidence intervals, reflecting greater precision in estimating the true cure rate.
Hypothesis Testing: By examining the confidence intervals, we can determine if the true cure rate of 50% falls outside any of these intervals, which would suggest that we can reject the null hypothesis. If 50% falls within all intervals, we fail to reject the null hypothesis.