Question

In a Washington Post/Kaiser Family Foundation Poll conducted from January through March 2015, 20% of women (ages 17‑26) who attended college during the past 4 years say they were sexually assaulted. The poll surveyed 514 randomly selected females.

The 90% confidence interval for the proportion of women (ages 17‑26) who attended college during the past 4 years and say they were sexually assaulted is (.171, .229).

1. If another survey done that year reported that only 15% of this population reported being sexually assaulted, does that report agree with the confidence interval? Why or why not?
2. According to the confidence level, is it impossible that the 15% rate could be correct even with the confidence interval generated? Why or why not? (Write carefully! Your confidence level must be central to your reasoning!)

Answer 1

The 90% confidence interval in percentage is (17.1%,22.9%) which means that we are 90% confident that the true percentage of women (ages 17‑26) who attended college during the past 4 years and say they were sexually assaulted is within (17.1%,22.9%).

Now the report that only 15% of this population reported being sexually assaulted does not agree with the confidence interval, as 15% is well outside the lower limit of the confidence interval.

90% confidence is not the chance its how confident are we with the interval, it is not impossible that the 15% rate could be correct,as we are only 90% confident and not 100%.