MATH 225N Week 6 Confidence Intervals Questions and Answers (Chamberlain College of Nursing)

1. On a busy Sunday morning, a waitress randomly sampled customers about their preference for morningbeverages, specifically, she wanted to find out how many people preferred coffee over tea.The proportion ofcustomers that preferred coffee was 0.42 with a margin of error 0.07.Construct a confidence interval for the proportion of customers that preferred coffee.(0.42 - 0.07), (0.42 + 0.07)= (0.35), (0.49)2.A company sells juice in 1quart bottles. In a quality control test, the company found the mean volume ofjuice in a random sample of bottles was X = 31 ounces, with a marginal error of 3 ounces.Construct a confidence interval for the mean number of ounces of juice bottled by this company.(31-3), 31+3)= (28), (34)3. Randomly selected employees at an office were asked to take part in a survey about overtime.The officemanager wanted to find out how many employees worked overtime in the last week.The proportion ofemployees that worked overtime was 0.83, with a margin of error of 0.11.(0.83 - 0.11), (0.83 + 0.11) =(0.72), (0.94)4. A random sample or garter snakes were measured, and the proportion of snakes that were longer than 20inches in length recorded.The measurements resulted in a sample proportion of p = 0.25 with a samplingstandard deviation of Op = 0.05.Write a 68% confidence interval for the true proportion of garter snakes that were over 20 inches in length.(.25 - .05). (.25 + .05)= (0.20), (.30)5. The average number of onions needed to make French onion soup from the population of recipes isunknown.A random sample of recipes yields a sample mean of x = 8.2 onions.Assume the samplingdistribution of the mean has a standard deviation of 2.3 onions.Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions.Since 95% falls in 2 SD's the calculation would be (8.2 - 4.6) "4.6 is the margin of error", (8.2 + 4.6) =(3.6) ,(12.8)