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STATS Six Problems Set

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Question;For each of the following problems (except problem 5), conduct the tests by using both the criticalregion method and by calculating a p-value.1. A company packages a lubricant in containers that hold 10 liters. A random sample of 10containers has contents of 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Assume thecontents to be normally distributed. A statistical study is to be conducted in order to test that theaverage content for these containers is 10 liters.(a) Carry out the test using a 1% significance level.(b) Calculate a 99% confidence interval for the average content.(c) Do any of your conclusions from parts (a) or (b) contradict each other? Why or why not?2. A new alloy is proposed for use in protecting inner walls of freight containers from rupture. Theengineering design specification requires a mean penetration of no greater than 2.250mm when abeam of specified weight and size is rammed into the wall at a specified velocity. Sixty test runsresulted in an average penetration of 2.255 mm and a standard deviation of 0.041 mm. Does it appearfrom these data that the design specifications are being met? Use? = 0.01.3. A study is performed to determine whether the amount of airborne bacteria is larger in carpetedrooms versus uncarpeted rooms. The data below was collected in a hospital for 8 carpeted rooms aswell as 8 uncarpeted rooms:Carpeted:Uncarpeted:11.812.18.28.37.13.813.07.210.812.010.111.114.610.114.013.7Does there appear to be a higher average amount of bacteria in carpeted rooms than in uncarpetedrooms? Test using? = 0.10. Concentrations are assumed to be normally distributed.4. Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concernin a number of different locales. An article published the accompanying data on the concentration (innanograms/m3) measured both indoor and outdoor for a sample of 10 houses within a certain region.IndoorOutdoor1.07.112.08.093.09.084.12.165.12.12House6.12.157.13.108.14.189.15.1710.15.20Using? = 0.05, is there a significant difference in the average amount of concentration indoors vs.outdoors? Assume measurements to be normally distributed.5. A post-mix beverage machine is adjusted to release a certain amount of syrup into a chamberwhere it is mixed with carbonated water. A random sample of 25 beverages was found to have amean syrup content of 1.098 fluid ounces and a standard deviation of 0.10 fluid ounces. Assume thecontents to be normally distributed. The interest is to test whether the mean amount of syrupdispensed is 1.0.(a) State appropriate null and alternative hypotheses. Do not conduct the test.Page 1 of 2(b) Using the O-C curves from class, is the sample size of 25 adequate if we wish to detect adifference of as much as 0.05 in the mean amount dispensed with a probability of 0.90? (i.e. thepower of the test is 90%). Use? = 0.05.(c) Again, using the O-C curves, how is n affected if we reduce the power to 80%?6. Many banks once required that customers wait in separate lines at each teller's window, but mosthave now changed to a single main waiting line. Why did they make that change? The mean waitingtime didn't change, because the waiting-line configuration doesn't affect the efficiency of thetellers. They changed to the single line because customers prefer waiting times that are moreconsistent with less variation. Thus thousands of banks made a change that resulted in lowervariation (and happier customers), even though the mean waiting time was not affected. To test this, abank manager whose bank still uses the multiple line system, knows that the standard deviation ofwaiting in line for service, during a Friday afternoon, is about 10 minutes per customer. Hoping toimplement a new policy of single line service, the waiting times for a sample of 25 customers on aFriday afternoon using a single line were observed by a pilot study and the standard deviation wascalculated to be 6.5 minutes. Using hypothesis testing, and assuming that waiting times are normallydistributed, should the manager adopt the new single line policy based on this pilot study? Use? =0.05.

Paper#61782 | Written in 18-Jul-2015

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