Consider roulette, a popular game that can be found in most casinos around the world. In the game, a small ball is rolled within a spinning wheel that contains differently colored (red, black, and green) and numbered markers (0, 00, and 1–36). Half of the numbers, 1–36, are red and the other half are black. In European versions of the game, there is a 0 that is green, and in American versions, there is a 0 and a 00 that are green. Before the wheel is spun, the players will place their bets on either a color, number, or a combination of both, and each choice presents a different set of odds. For example, placing a bet on an “even” number or on “red” will pay out 1:1. A player can choose to bet on a single number too, with a payout of 35:1. A player could also choose a set of numbers, such as 1–12 for a payout of 2:1. If a player bet $100 for each of these examples and won, the winnings would be $100, $3,500, and $200 respectively.With these payouts, it may seem that the odds are as even for the player as they are the casinos, almost as if it was a fair game. But, someone with an understanding of probability will realize that the casinos have a slight advantage that—if played out time and time again—will always favor the casino and create profits for them. If there were only 36 numbers, the risks would be evenly distributed for most picks, but you must also include the 0 and the 00 into the equation. The odds for the player of a 1:1 bet are not 50/50—they are 47.4% for the player and 52.6% for the casinos for an American style roulette table.In this Discussion, you will examine a well-known statistical problem that represents the concepts of probability and the benefits of how this concept can influence decision making.To prepare for this Discussion: Review this week’s Learning Resources, focusing in particular on the Monty Hall Dilemma and Probability section.Consider your initial thoughts on the Monty Hall dilemma as you are introduced to the concept, and be mindful of how your assumptions might change after you have finished reviewing the resources.Review the Academic Writing Expectations for 2000/3000-Level Courses, provided in this week’s Learning Resources.By Day 3Post a 150- to 225-word (2- to 3-paragraph) explanation of how the Monty Hall dilemma can be applied to management decisions. In your explanation, address the following:Explain your thoughts on the Monty Hall dilemma, including what the correct choice is and why, any challenges you may have faced in accepting the answer, and how your opinion may have changed while reviewing this week’s Learning Resources. For example, do you still have a difficult time accepting the results?Managers often make decisions about problems that have similar amounts of uncertainty as the Monty Hall dilemma. What can this exercise teach them about making decisions under uncertainty, and what would be an example of this lesson in practice in a business environment?To support your response, be sure to reference at least one properly cited scholarly source.Refer to the Week 2 Discussion Rubric for specific grading elements and criteria. Your Instructor will use this grading rubric to assess your work.Read some of your colleagues’ postings.By Day 5Respond with at least 75 words (1 paragraph) each to two or more of your colleagues’ postings by doing one of the following:Explain any similarities or differences you experienced in how challenging you thought it was to accept the answer or in how your opinion may have changed while reviewing this week’s Learning Resources.Explain whether you agree or disagree with your colleague’s assertion of what lessons can be learned from the Monty Hall dilemma or what an example of this lesson would be in a business environment.

A t test examines if two means (averages) are reliably different from each other; that is, whether any significant differences exist between the means of samples from different populations. For example, to what extent is the output of a local office which applied an IT solution different than the output of other local offices which did not apply the IT solution? Also, if you wanted to test whether the average IQ score of a group of students differs from 100, you may use a t test. A t test does more than just compare means; as an inferential statistic, t tests allow researchers to make inferences about the populations beyond their sample data.For this Assignment, you will use the IT Security database and conduct two t tests: (a) one-sample t test and (b) paired-samples t test and prepare an APA results write-up for each test.To prepare for this Assignment:Review the media programs:Introduction to Hypothesis TestingThe t StatisticThe t Test for Related SamplesEstimationReview Lesson 22, "One-Sample t Test.” Then conduct a one-sample t test using the IT Security Dataset from this week’s Learning Resources.Pay particular attention to the sections titled “Writing an APA Results Section” (on pages 119-120) and “An APA Results Section” (on page 167) in the Green and Salkind text.Review Lesson 23, “Paired-Samples t Test.” Then conduct a paired-samples t test using the IT Security Dataset.Pay particular attention to the section titled “An APA Results Section” (on page 122) in the Green and Salkind text.Review the Assignment Exemplar provided in this week’s Learning Resources.Submit a 5- to 6-page paper using the Assignment Exemplar.Your paper must include the following elements:An APA Results section for each t test. (See examples of APA Results sections in Lesson 22 (one-sample t test) and Lesson 23 (paired-samples t test) of the Green and Salkind text.)The critical elements of your SPSS output, including:A properly formatted research questionA properly formatted H10 (null) and H1a (alternate) hypothesisA descriptive statistics narrative and properly formatted descriptive statistics table (see page 148 of the Green and Salkind text)A properly formatted histogram for the one-sample t test (see page 149 of the Green and Salkind text)A properly formatted box plot for the paired-samples t test (see page 154 of the Green and Salkind text)A properly formatted inferential APA Results Section (see page 149 of the Green and Salkind text) for each testAn appendix including the SPSS output generated for descriptive and inferential statistics (see SPSS output on page 148 of the Green and Salkind text)