Final answer:
To construct a 95% confidence interval for the proportion of treated subjects who experienced headaches, calculate the point estimate, margin of error, and construct the interval.
Step-by-step explanation:
To construct a 95% confidence interval for the proportion of treated subjects who experienced headaches, we need to find the point estimate, margin of error, and construct the interval.
a) The point estimate is the number of subjects who experienced headaches divided by the total number of subjects treated with oxycontin. So, the point estimate is 16/227.
b) The margin of error can be calculated using the formula:
E = Z * sqrt((p*(1-p))/n), where Z is the Z-score corresponding to the desired confidence level (95% in this case), p is the point estimate, and n is the sample size. The margin of error gives us the range of values within which the true population proportion is likely to fall.
c) To construct the confidence interval, we use the formula:
CI = p +/- E, where CI is the confidence interval, p is the point estimate, and E is the margin of error. Substituting the values, we can calculate the lower and upper bounds of the interval.
d) A correct interpretation of the confidence interval would be: We are 95% confident that the true proportion of treated subjects who experienced headaches is between the lower and upper bounds of the interval.