Final answer:
To construct a 90% confidence interval for the proportion of adverse reactions, the formula p±z*sqrt((p*(1-p))/n) using the sample proportion as the point estimate is applied. The confidence interval indicates where the true population proportion is likely to be based on the sample data.
Step-by-step explanation:
To construct a 90% confidence interval for the proportion of adverse reactions caused by the drug, we can use the formula for a confidence interval for a population proportion. The formula is given by:
p±z*sqrt((p*(1-p))/n)
where p is the sample proportion, z is the z-value corresponding to the desired confidence level (in this case, 90%), n is the sample size, and sqrt stands for square root.
The best point estimate of the population proportion p is simply the sample proportion, which is the number of successes (patients with the adverse reaction) divided by the total number of trials (patients treated).
To calculate this for the given data:
- Number of patients with adverse reaction (successes) = 151
- Total patients treated (trials) = 4593
- Sample proportion (p) = 151/4593
Substitute these values into the formula to calculate the confidence interval.
Explanation of a confidence interval: A confidence interval gives a range of values within which we can say with a certain level of confidence, here 90%, that the true population parameter lies. It's not a guarantee that the true parameter is within this range but indicates where the parameter is likely to found based on our sample data.