1) The distribution of diastolic blood pressure (BP) for adults in the U.S. has a mean of 80 mmHg (millimeteres of mercury) and a standard deviation of 12 mmHg. (Note: Diastolic BP is the lower number in a blood pressure measurement.) A U.S. adult had a diastolic BP of 92 mmHg. If the distribution of diastolic BP for adults in the U.S. is bell-shaped, then approximately what proportion of adults in the U.S. have a diastolic blood pressure above 92 mmHg?
2) You are on a committee at your school to help guide decisions about various cost-cutting measures. One proposal is to decrease the number of publications of the school newspaper from two issues per week to just one per week. You suggested taking a survey of students to gather opinions. One question that will be asked is "Do you support the reduction of the number of issues of the school newspaper one issue per week as part of cost-cutting measures?"
a) In designing this study, you need to decide on the number of students to survey. With the help of a faculty advisor, you decide that your estimated population proportion should have a margin of error of +/- 6% with a 95% level of confidence. What is the minimum number of students that should be surveyed?
b)The survey was sent out and 200 of the students actually completed the survey (so some non-participation). Of these 200 students, 114 said they would favor the reduction of issues, for an estimated proportion of 0.57 or 57%. Provide first the approximate conservative 95% margin of error and then use it to report the corresponding confidence interval estimate.