Practice Problem 1 Your instructor claims 50% of the beads in a container are red. A random sample of 251 beads is selected, of which 107 are red. Calculate and interpret a 90% condence interval for the proportion of red beads in the container. Use your interval to comment on this claim. Practice Problem 2 In New York city on October 23"'1 , 2014, a doctor who had recently been treating Ebola patients in Guinea went to the hospital with a slight fever and was subsequently diagnosed with Ebola. Soon thereafter, an NBC 4 New York Marist Poll Found that 82% of New York favored a mandatory 21- day quarantine for anyone who has come in contact with an Ebola patient. This poll included responses of 1042 New York adults. 1) What is the point estimate in this case, and is it reasonable to use a normal distribution to model that point estimate? 2) Estimate the standard error of 13 = 0.82 from the Ebola survey. 3) Construct a 95% condence interval for p, the proportion of New York adults who supported a quarantine for anyone who has come into contact with an Ebola patient. Practice Problem 3 The general Social Survey asked the question: "for how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. 1) Interpret this interval in the context of the data. 2) What does "95% confident" mean? Explain in the context of the application. 3) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this interval be smaller or wider than the 95% confidence interval? 4) If a new survey were to be done with 500 Americans, do you think the standard error of the estimate be large, smaller, or about the same.Practice problem 4 We want to construct a 95% condence interval for the true proportion of all adult males who have spent time in prison, with a margin of error of 0.02. From previous studies, we believe the proportion to be somewhere around 0.07. What is the required sample size? Practice problem 5 You buy a package of 122 Smarties and 19 of them are red. What is a 95% confidence interval for the true proportion of red Smarties?Practice Problem 6 The Peacock Electric Company thinks that 40% of their customers would be interested in bundling solar power purchasin with their electric bill. A random sample of 400 households reveals that 110 of t e households are interested in this. 1) Construct a 99% condence interval for the true proportion of households interested in bundling solar with their utilities. 2) Do you feel the company is accurate in its belief about the proportion of customers who have interest in bundling solar power with their utilities? Justify your