Statistics Exam (Spring 1997) - Confidence Intervals, Hypothesis Testing, ANOVA - Prof. Gr, Exams of Probability and Statistics

Download Statistics Exam (Spring 1997) - Confidence Intervals, Hypothesis Testing, ANOVA - Prof. Gr and more Exams Probability and Statistics in PDF only on Docsity! STAT 401 (Spring 1997) Page 1 of 2 Instructor: Dr. A. Kagan Final Exam, 05/20/97 [15] l. In a study of a special brand of tires, the life time (in thousand miles) data of 15 tires were collected. The sample mean turned 62.3, the sample sd 3.8. Assuming normality, construct 90% confidence intervals for the mean life time of tires under study arid for its standard deviation. [15] 2. If the population (not sample) standard deviation of the tires life time is 4.0 (in thousand miles) what is the minimum number of tires to be tested in order to ensure that a 95% confidence interval for the mean life time have the length < 3.0. [20] 3. Two drugs with unknown efficiencies (probabilities of a success) are used for treatment of an illness. A group of 130 patients was treated with the first drug; 90 patients showed significant improvement (a success). Another group of 140 patients was treated with the second drug; 94 patients showed significant improvement. Using the normal approximation, construct 90% confidence intervals for the efficiencies of the drugs. Construct a 80% confidence interval for the difference between the efficiencies. [20] 4. A company advertising a special food, uses the slogan "With our food, you will loose 10 pounds in 30 days." The following data relate to 9 people who were with the program for at least 30 days, the numerator (resp. denominator) being the person's weight (in pounds) before entering the program (resp. after 30 days with the program): 196/187, 194/176, 208/198, 224/208, 208/196, 196/180, 206/200, 210/188, 184/176. Do the data support the above slogan? State the problem as one of testing a statistical hypothesis, formulate the proper null hypothesis and the alternative. Test the hypothesis at .95 and .90 levels. Estimate the p-value of the data. Explicitly state the assumptions about the population you are making.