Final answer:
To determine a 90% confidence interval for the population proportion of women who most feared breast cancer, we calculate the standard error, then the margin of error. Finally, we construct the confidence interval using the sample proportion and the margin of error. The correct interpretation is that we can be 90% confident that the true population proportion lies within the constructed interval.
Step-by-step explanation:
To determine a 90% confidence interval for the population proportion of women who most feared breast cancer, we first need to calculate the standard error. The formula for the standard error is:
SE = sqrt((p * (1-p)) / n)
where p is the sample proportion (0.61), and n is the sample size (1000). Substituting the values into the formula:
SE = sqrt((0.61 * (1-0.61)) / 1000) = 0.015
Next, we can calculate the margin of error (ME) using the formula:
ME = z * SE
where z is the z-score corresponding to the desired confidence level (90% confidence level corresponds to a z-score of approximately 1.645). Substituting the values into the formula:
ME = 1.645 * 0.015 = 0.025
The 90% confidence interval is then given by:
CI = sample proportion +/- ME
Substituting the values:
CI = 0.61 +/- 0.025
CI = (0.585, 0.635)
(a) A 90% confidence interval for the population proportion of women who most feared breast cancer is (0.585, 0.635).
(b) The correct interpretation of the interval is that we can be 90% confident that the true population proportion of women who most feared breast cancer lies within the interval of 0.585 to 0.635.