At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
1. The Aid to Families with Dependent Children (AFDC) program has an overall error rate of 4% in determining eligibility. The state of California uses sampling to monitor its counties to see whether they exceed the 4% error rate, which can result in economic sanctions. In one county, 9 cases out of 150 were found to be in error.
(a) Find a 95% confidence interval for the error rate for the county (proportion of all cases in error).
(b) In 1982 the California legislature mandated that a 95% confidence interval be used in studying error rate. Based on your answer in part (a), would you conclude that the error rate for the county is above the 4% rate?
2. To estimate the proportion p of passengers who had purchased tickets for more than $400 over a year's time, an airline official obtained a random sample of 75. The number of those purchasing tickets for more than $400 was 45.
(a) What is a point estimate for p?
(b) Find a 90% confidence interval for p.