Based on data from the 2007 National Health Interview Survey, it is estimated that “10% of adults experienced feelings of sadness for all, most, or some of the time” during the 30 days prior to the interview. You interview a random sample of 68 people who have recently filed for unemployment benefits in your county, and ask this same question in your survey.

(a) Identify the implied target population for your study.

(b) If the proportion of your population with these feelings is the same as the 10% nationally, what is the probability that your sample will have 12 or more people with these feelings?

(c) What would you conclude if your sample did have 12 or more people with these feelings?

(d) If the true percentage of your population with these feelings is 10%, what is the probability that the sample percentage will differ from this by more than 5%?