1. The manager of the dairy section of a large supermarket took a random sample of 250 egg cartons and found that 40 cartons had at least one broken egg. a. Find a 90% confidence interval for IT. b. Find a point estimate for I, the proportion of egg cartons with at least one broken egg out of the population of all egg cartons stocked by this store. 2. A researcher wanted to compare unsafe radon levels in the Hyde Park region and the LaGrange regions. In the Hyde Park region, they randomly surveyed 186 homes and found that 30 had unsafe radon levels. In the LaGrange region, they surveyed 237 homes and found that 45 had unsafe radon levels. a. Should the researcher conclude that there is a difference in the proportion of homes with unsafe radon levels between the two regions at the 5% significance level? b. Find a 99% confidence interval for the difference in the proportion of homes with unsafe radon levels. 3. A random sample of 200 marriage license applications recorded in 1987, 62 of the women were at least one year older than the men, and in a random sample of 300 marriage license applications in 1997, 99 of the women were at least one year older than the men. At the 0.01 significance level, is the upward trend statistically significant? 4. A medical group studied the ailments of adults with diabetes. Of 8750 adults who are diabetic, 2100 have high cholesterol. Of 12, 350 adults who are not diabetic, 1482 have high cholesterol. a. Find a 95% confidence interval for the difference in proportion of adults who are diabetic and have high cholesterol and the proportion of adults who are not diabetic and have high cholesterol. b. At a = 0.01, do the data indicate that adults who are diabetic have high cholesterol more often than those adults who do not have diabetes