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?5. A study of 415 students showed that they have seen an average 3000 hours of TV. If the sample standard deviation is 400, find the 90% confidence level of the mean for all students. If a parent claimed that his children watched 2000 hours, would the claim be believable? 6. A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from the previous study is 7.8 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.9 hours? 7. Find the 99% confidence interval for the variance and standard deviation of the ounces of coffee that a machine dispenses in a 12-ounce cups. Assume the variable is normally distributed. Use the following data to find the confidence interval. 12.03 12.10 12.02 11.98 12.00 12.05 11.97 11.99 8. A service station advertises that customers will have to wait no more than 35 minutes for an oil change. A sample of 34 oil changes has a standard deviation of 4.8 minutes. Find the 95% confidence interval of the population standard deviation of the time spent waiting for an oil change.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
