1. A congressional committee wishes to estimate the average annual subsidy received by tenant farmers in a southern state. A random sample of 495 farms is taken, the sample mean is found to be $7,850 with a sample standard deviation of $750. Compute the 99% confidence interval estimate of the annual subsidy?
2. Business statistics students claim that they spend at least 3 hours studying for and working through statistics practice problems per week. A random sample of 44 college students enrolled in a business statistics course was asked how many hours he or she spent practicing working statistics problems. The sample average was found to be 2.4 hours per week with a standard deviation of 1.25 hours. Using the p-value method and α = .01, determine if the students are studying the amount of time that was claimed.
3. You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process to a method that you think will reduce the mean time, from the order to the completion of the delivery, down from the current 25 minute delivery time. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a standard deviation of 6 minutes. Can you conclude that the new delivery process has reduced the population mean delivery time? Use the p-value method and a significance level of 2.5% to answer this question.
4. A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within $50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $400. How large of a sample size is needed?
5. Two hundred people are randomly chosen at a shopping mall to taste-test a new brand of fruit drink. They are asked to rate the drink on a scale from 1 to 5, with 5 being very good and 1 being very bad. The results of the survey reveal that the sample average rating is 3.63 with a standard deviation of 1.22. Compute the 90% confidence interval estimate of the mean drink rating?