ASSIGNMENT CHAPTER 8 Statistical Methods NAME M S 357 358 ELEMENTS 8 11 8 13 8 14 M S 363 364 LARGE SAMPLE 8 24 8 26 8 29 8 30 8 32 M S 371 372 P VALUE 8 48 8 51 M S 378 379 SMALL SAMPLE 8 66 8 67 8 68 M S 383 386 PROPORTIONS 8 74 8 78 8 80 M S 392 394 POWER OF A TEST 8 95 M S 397 401 POPULATION VARIANCE 8 111 8 113 MS 357 358 8 11 2 points Use of herbal therapy According to the Journal of Advanced Nursing January 2001 45 of senior women i e women over the age of 65 use herbal therapies to prevent or treat health problems Also a senior women who use herbal therapies use an average of 2 5 herbal products in a year a Give the null hypothesis for testing the first claim by the journal b Give the null hypotheses for testing the second claim by the journal ANSWERS 8 13 2 points DNA reading tool for quick identification for species A biologist an a zoologist at the University of Florida were the first scientists to test the effectiveness of a high tech handheld device designed to instantly identify DNA of an animal species PLOS Biology Dec 2005 They used the lusks with brightly colored shells The scientists discovered that the error rate of the device is less than 5 percent Set up the null and alternative hypothesis if you want to support your findings ANSWER 8 14 3 points Susceptibility to hypnosis The Computer Assisted Hypnosis Scale CAHS is designed to measure a person s susceptibility to hypnosis CAHS scores range from 0 no susceptibility to hypnosis to 12 extremely high susceptibility to hypnosis Psychological Assessment March 1995 reported that University of Tennessee undergraduates had a mean CAHS score of m 4 6 Suppose you want to test whether undergraduates at your college or university are more susceptible to hypnosis than the University of Tennessee undergraduates a Set up H 0 and H a for the test b Describe a Type I error for the test c Describe a Type II error for the test ANSWERS MS 363 365 8 24 2 points A random sample of 64 observations produced the following summary statistics x 323 and s 2 034 a Test the null hypothesis that m 36 against the alternative hypothesis that m 36 using a 10 b Test the null hypothesis that m 36 against the alternative hypothesis that m 36 using a 10 interpret the result ANSWERS 8 26 3 points Latex allergy in health care workers Refer to the Current Allergy Clinical Immunology March 2004 study of 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder on latex gloves used per week by the sampled workers is summarized as follow x 19 3 and 11 9 Let m represent the mean number of latex gloves used per week by all hospital employees Consider testing H 0 m 20 against H a m 20 n s a Give the rejection region for the test at a significance level of a 01 b Calculate the value of the test statistics c Use the results from parts a and b to draw the appropriate conclusion ANSWERS 8 29 2 points Post traumatic stress of POWS Psychological Assessment March 1995 published the results of a study of World War II aviators captured by German forces after having been shot down Having located a total of 239 World War II aviator POW survivors the researchers asked each veteran to participate in the study 33 responded to the letter of invitation Each of the 33 POW survivors was administered the Minnesota Multiphasic Personality Inventory one component of which measures level of post traumatic stress disorder PTSD Note the higher the score the higher is the level of PTSD The aviators produced a mean PTSD score of x 9 00 and a standard deviation of 9 32 s a Set up the null and alternative hypotheses for determining whether the true mean PTSD score of all World War II aviator POWs is less than 16 Note PTSD score established for the Vietnam The value 16 represents the mean POWs b Conduct the test from part a using a 10 What are the practical implications of the test ANSWERS 8 30 2 points Point spreads of NFL games During the National Football League NFL season Las Vegas oddsmakers establish a point spread on each game for betting purposes For example the Indianapolis Colts were established as 7point favorites over the Chicago Bears in the 2007 Super Bowl The final scores of the NFL games were compared against the final point spreads established by the oddsmakers in Chance Fall 1998 The difference between the outcome of the game and the point spread called a point spread error was calculated for 240 NFL games The mean and standard deviation of the point spread error are x 1 6 and 13 3 Use this information to test the hypothesis that the true mean point spread error for all NFL games is 0 Conduct the test at a 01 and interpret the result s Answer 8 32 2 points Cooling method for gas turbines During periods of high demand for electricity especially in the hot summer months the power output from a gas turbine engine can drop dramatically One way to counter this drop in power is by cooling the inlet air to the turbine An increasingly popular cooling method uses high pressure inlet fogging The performance of a sample of 67 gas turbines augmented with high pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power Jan 2005 One measure of performance is heat rate kilojoules per kilowatt per hour Heat rates for the 67 gas turbines saved in the GASTURBINE file are listed in the table Suppose that a standard gas turbine has on average a heat rate of 10 000 kJ kWh a Conduct a test to determine whether the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10 000 kJ kWh Use a 05 b Identify a Type I error for this study Indentify a Type II error GASTURBINE 14622 13196 11948 11289 11964 10526 10387 10592 10460 10086 14628 13396 11726 11252 12449 11030 10787 10603 10144 11674 11510 11842 10481 9421 16243 10946 10656 9812 9105 14628 10508 10604 10270 10529 11360 11136 10814 13523 9669 9643 9115 9115 10233 10186 9918 9209 12766 8714 9469 11948 10360 14796 12913 12270 11289 11183 10951 9722 11588 10888 9738 9295 9532 9933 9152 9295 12414 ANSWERS MS 371 372 8 48 4 points Prices of hybrid cars BusinessWeek com provides consumers with retail prices of new cars at dealers from across were obtained from a sample of 160 dealers These 160 prices are saved in the HYBRIDCARS file a Give the null and alternative hypotheses for testing whether the mean July 2006 dealer price of the Toyota Prius m differs from 25 000 b Data from the HYBRIDCARS file were analyzed with …