1. In a certain countrywide school district, a survey of 280 students showed that 34% carried their lunches to school. Find the 99% confidence interval of the true proportion of students who carried their lunches to school. If the cafeteria manager wanted to be reasonably sure that all the children who didn't bring their lunches could purchase a lunch, how many lunches should she plan to make each day. Explain your answer. 2. A medical researcher wishes to determine the percentage of females who take vitamins. He wishes to be 95% confident that the estimate is within 4 percentage points to the true proportion. A recent study of 210 females showed that 20% took vitamins. a) How large should the sample size be? b) If no estimate of the sample proportion is available, how large should the sample be? 3. The number of grams of carbohydrates in a 12-oz serving of a regular soft drink is listed here for a random sample of sodas. Estimate the mean number of carbohydrates in all brands of soda with 90% confidence. 48 37 52 40 43 46 41 38 41 45 45 33 3 52 45 41 34 46 40 4. A sample of 6 college wrestlers had an average weight of 254 lbs. with a sample standard deviation of 11.4 lbs. Find the 95% confidence interval of the true mean weight of all college wrestlers. If a coach claimed that the average weight of the wrestlers on his team was 301, would the claim be believable?Chapter 7 Test 4 CI Directions: Use the correct distribution tables (Normal, studentt, or Chisquare) to correctly construct the following condence intervals. Please show all steps, including using the correct formulas (set up), all appropriate work and hox in your final condence interval. (You don't need to cop).' the problem, just write out the needed given information to do the interval or get your need answer). Note: Not all problems will be condence intervals