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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.