Research_Methods

Research Methods and Business Decisions In this paper, we will research statistical data that requires a decision, and we will be using probability concepts to formulate this decision. We will also explain the research methods and the process for limiting the uncertainty in the decision. We will research statistical data regarding guessing the right answer in the University of Phoenix final exam. I have to decide whether to guess the answers for the exam and not worry about studying, and by that risk passing the exam, or put effort and time to study hard for this exam. We will be calculating the probability of each success. The data follows the binomial distribution for the following reasons: There are only two possible outcomes; an outcome on each trial of the experiment is classified into one of two mutually exclusive categories – a success or a failure (University of Phoenix, 2010). There are a fixed number of trials limited to the number of questions in the final exam. The probability of a success and failure stays the same for each trial; it is one correct answer for each question in multiple choices composed of four answers. It is 25% or 0.25. The trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. Part of statistical modeling is using the right analytical tool for the appropriate situation (University of Phoenix, 2010). The binomial probability is the most effective in our case. To construct the binomial probability of the right guesses in the final exam, we can use the following binomial probability formula: P(x)=nC_x π^x 〖(1-π)〗^(n-x) Alternatively, we can use an excel spreadsheet and compute the probability using the BINOMDIST formula. The BINOMDIST formula has four parameters as follows: 1. The number of successes in trials. 2. The number of independent trials. 3. The probability of success on each trial. 4. A discreet or cumulative probability. In our case, we need to calculate the number of successes. We will suppose that we have 30 questions in the final exam. The number of independent trials is 30 questions, and the probability of success in each trial is 0.25. We will calculate the discreet probability for each question. The following table shows the statistical data for our case: X P(X) 0 0.000178582 1 0.001785821 2 0.008631468 3 0.026853455 4 0.060420274 5 0.104728475 6 0.145456215 7 0.166235674 8 0.159309188 9 0.129807486 10 0.09086524 11 0.055069843 12 0.029064639 13 0.013414449 14 0.005429658 15 0.001930545 16 0.000603295 17 0.00016561 18 3.98692E-05 19 8.39351E-06 20 1.53881E-06 21 2.44256E-07 22 3.33076E-08 23 3.86175E-09 24 3.75448E-10 25 3.00358E-11 26 1.92537E-12 27 9.50802E-14 28 3.39572E-15 29 7.80626E-17 30 8.67362E-19 Where P(x) =BINOMDIST (A1 to A30, 30, 0.25, FALSE). The following chart represents the distribution of the probability: Based on the above calculations the probability of guessing between seven and eight right answers is the highest at 0.16. Moreover, this probability decreases when the number of questions increases. The probability will be near zero for the trials that are above 17 to 30. All of our decisions involve risk and our own personal tolerance for risk. Statistical tools for analyzing data give us a means of minimizing that risk. Based on the above analysis of available data, I should not depend on guessing the right answers to my final exam, instead I should prepare for the exam carefully. References University of Phoenix. (2010). Week Three supplement: Applied Business Research and Statistics. Retrieved from University of Phoenix, Week Three, QNT/561- Applied Business Research and Statistics Course Web site.