Assignment 1.docx

ASSIGNMENT 1 & 2 ADVANCE STATISTICS Due Date : September, 20th ,2018 Hypothesis Testing One Parameter 1. Mountain States Surgery Center – The Mountain States Surgery Centre in Denver, Colorado, performs many knee replacement surgery procedures each year. Recently, research physicians at Mountain States have developed a surgery process they believe will reduce the average patient recovery time. The hospital board will recommend the new procedure unless there is substantial evidence to suggest that it is better than the existing procedure. Record indicate that the current mean recovery rate for the standard procedure is 142 days, with a standard deviation of 15 days. To test whether the new procedure actually results in a lower mean recovery time, the procedure was performed on a random sample of 36 patients. Sample mean is 140.2 days. The desire significant level is 0.05. Please specify : a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision e. Draw a conclusion 2. Dodger Stadium Parking – The parking manager for the Los Angeles Dodgers baseball team has studies the exit times for cars leaving the ballpark after a game and believes that recent changes to the traffic flow leaving the stadium have increased, rather than decreased, average exit times. Prior to changes the previous mean exit time per vehicle was 36 minutes, with a population standart deviation equal to 11 minutes. To test the parking manager’s belief, a simple random sample of n=200 vehicles is selected, and a sample mean of 36.8 minutes is calculated. Using an alpha 0.05 level. Please conduct the hypothesis test. a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision e. Draw a conclusion 3. The Potlatch Corporation – The Potlatch Corporation is a wood products company with lumber, plywood, and paper plants in several areas of the United States. At its St. Maries, Idaho, plywood plant, the company makes plywood used in residential and commercial building, One product made at the St. Maries plant is 3/8-inch plywood which must have a mean thickness of 0.375 inches. The standard deviation is known to be 0.05 inch. Before

sending a shipment to customers, Potlatch managers test whether they are meeting the 0.375 inch requirements by selecting a random sample of n=100 sheet of plywood and collecting thickness measurements. Please specify : a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision e. Draw a conclusion

Hypothesis Testing Two Parameters 1. Healthcare Associates – Healthcare Associates operate 33 medical clinic in Minnesota and Winconsin. As part of the company’s ongoing efforts to examine its customer service, Healthcare worked with an MBA class at one of the Minnesota university on a project in which a team of students observed patients at the clinics to estimate the difference in mean time spent per visit for men and women patients. Previous studies indicate that the standard deviation is 11 minutes for males and 16 minutes for females. Simple random samples 100 males and 100 females. Sample means are 34.5 for males and 42.4 minutes for females. To develop a 95% confidence interval estimate for the difference in mean times. Please determine : a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision e. Draw a conclusion 2. Sneva Pharmaceutical Research – The head of research and development at Sneva Pharmaceutical Research is interested in estimating the difference between individuals age 50 and under and those over 50 years old with respect to the mean time from when a patient takes a new medication until the medication can be detected in the blood. Once she estimates the difference, if a difference does exist, the company can use this information to guide doctors in how to advise their patients to use this modification. A simple random sample of six people age 50 or younger and eight people over 50 participated in the study. The research manager wishes to have a 95% confidence interval estimate. Sample means and standard deviation (s1) for younger people are 13.6 minutes and 3.1 minutes. Morever, sample means and standard deviation (s2) for older people are 11.2 minutes and 5 minutes Please specify : a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision

e. Draw a conclusion 3. Color Printer Ink Cartridges – A recent Associated Press news story out of Brussels, Belgium, indicated the European Union was considering a probe of computer makers after consumers complained that they were being overcharged for ink cartridges. Companies such as Canon, Hewlett-Packard, and Epson are the printer market leaders and make most of their printer-related profits by selling replacement ink cartridges. A simple random sample of 10 users was selected, and the users were given a name brand cartridge. A second sample of 8 users was given generic cartridges. Both groups used their printers until the ink ran out. The number of pages printed was recorded. The samples are independent because the pages printed by users in one group did not in a way influence the pages printed by users in the second group. The means computed from the group one and two samples are 322.5 pages and 298.3 pages. The population standard deviation are S1 = 48.3 pages and S2=53.3 pages. The test will be conducted using 95% confident interval. Please determine : a. The null and alternative hypothesis b. Construct the rejection region c. Compute the test statistic d. Reach a decision e. Draw a conclusion