Statistics with Excel

#3

#4

Final Prob4.) The manager of a project determined some time ago that the most critical task in the timely completion of a project is the use of a special instrument, a confusitron, that has an uncertain completion time (a random variable in terms of hours). He asks you, a confusitron expert, to use your experience to specify a discrete triangular probability distribution of outcomes--most like time to complete, pessimistic time to complete, and optimistic time to complete. Recently the project manager has learned that there is another equally critical task--framis-validation. This task occurs immediately after the confusitron. You are also a framis-validation expert. The project manager asks you for a similar discrete triangular distribution of outcomes (see below). He then asks you to create a random sample of 100 observations from this distribution: Confusitron Distribution of Hrs. Framis-Validation Distribution of Hrs. 1) Randomly sample 100 observations for both discrete triangular distributions of each task. Create a RV that is the sum of the tasks for each observation. Place the results in the designated area below. 2) Create a frequency distribution column graph of the 100 Sum observations below by determining the Sample Space for the RV; so, the bins for the column graph will be the unique sample space values of the graph. Make the first bin 0. (Hint: there should be 9 bin values, including 0) 3) What is the expected value of the Sum distribution? There are 2 theoretical ways to calculate it. Does it approximately match the average of your 100 observations (as it should)?

#8

Final Prob8.) After a National Championship season (2013) the W&M Ultimate Mixed Martial Arts (UMMA) team trainers, Lupe—heavy weight division, Abe—welterweight division, and Gene—flyweight division, were celebrating at the Blue Talon Bistro in Williamsburg, VA. The conversation started as pleasant chatter, but in minutes a roaring argument was blazing! The headwaiter finally asked the trainers if they could be quiet or leave. Calm returned to the table and the headwaiter asked what seemed to be the problem. Gene said that the group was arguing if there was a significant difference of performance by the fighters in the 3 weight divisions. The headwaiter, a retired data analytics professor at W&M, said: “I have a laptop, and Excel and Minitab. Why don’t we do a test of hypothesis that at least one of the weight divisions is better than the others over the entire 3 meets?” Lupe had a thumb drive of the points scored by 24 fighters at 3 meets in 3 UMMA weight divisions. Use the data provided to perform the test of hypothesis and use a level of significance of 0.05. You may use Excel or Minitab to test the hypothesis. If you use Minitab copy the output to this sheet. 1) Write the Null and Alternative Hypotheses below. 2) Is there was a significant difference in performance (average points) by the fighters in the 3 weight divisions. (Give me the value of a measure that you use to either reject the null hypothesis or not to reject the null hypothesis.)