Let me know if you have any questionplease do not forget to explain to me in details how did you get the answers as you can?you sholud know how to use stata program it called ststa C64The reading is: i attached it called the readingOLS Simple Regression_Part2_Hypothesis Testing (read the lecture slides to learn how to interpret hypothesis testing regression results in STATA

1. (6 points) How large would a potential Jackpot have to be in the California Mega Millions Lottery in order for the game to be fair? Present your computation and explain your reasoning in addition to stating your final answer. Note: A fair game is one in which in the long-run neither party (lottery company and players) has an advantage. 2. There are a number of probability claims made in the Lottery tips. In this problem, you will verify whether these claims are true. Consider the current rules (5/70 + 1/25) of the CA MEGA millions game. (a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that the five white numbers selected will all be even. (b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to approximate the probability that the sum of the five white balls will fall between 132 and 223 (both inclusive). Discuss the appropriateness of using the Central Limit Theorem in this case. If any of the assumptions of the theorem are violated, state what these assumtions are and discuss how extreme (mild, moderate, severe) the violation is. (c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether this tip only concerns the white balls or also the gold MEGA ball. i. Find the exact probability that in a given drawing at least one of the white numbers is a repeat from the last drawing. ii. Find the exact probability that in a given drawing at least one of the six balls drawn (five white and one gold) is a repeat of the last drawing. (d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA million lottery numbers (five white balls and MEGA ball) will be repeated in a drawing? Recall, that drawings take place bi-weekly and that assume that a year has 365 days (i.e., ignore leap years). 3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the advice of the lottery expert increase your chances of winning the lottery? (This is a multiple choice question - Yes/No answer ONLY.) 4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the statements made in the individual tips presented there generally truthful? Do they hold for general (future) drawings, and not just for data collected in the past? Is following this advice a good idea when playing the lottery? Explain why or why not. Take a stand and defend your position with a good logical argument using the methods of probability you have learned in this course. Provide as much numerical evidence as necessary (you may cite your results from problem 2) to support your 3 Math 161A - Fall 2020 M. Bremer claim(s). Make sure to provide a cohesive argument (using correct spelling and good grammar). 5. (5 points) To study whether the drawing of lottery numbers for the MEGA million game is truly random, we will consider some data. The data (which are available in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions between 5/17/2002 and 11/03/2020. Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on. Disclaimer: The data come from the New York State (not the California State) MEGA millions lottery. Like California, NY has changed the rules for the MEGA millions game several times over the last couple years. For instance, on October 19, 2013, they switched from drawing 55 white balls to drawing 75 white balls. On the same date, the number of possible MEGA balls were reduced from 45 to 15. Another rule change occurred in October 2017. Note: You are welcome to look at the raw data and/or create your own additional graphs if you wish, but that’s not required for this problem. Grading: Your work will be graded

To Prepare:Focus on and consider the evaluation needs for an institution. Centennial Community Association --Current Situation Recently, the neighborhood and nearby businesses have experienced an increase in vandalism, resulting in costly repairs. The recent economic downturn has also reduced home prices within the Centennial neighborhood. A proposal to construct a teen homeless shelter at the New Harbor Community Center has residents angry that their home investments will further decline because of a potential influx of young homeless teens, who they suspect are the perpetrators of most of the recent vandalisms. The overall opinion of residents in Centennial is that they enjoy having the New Harbor Community Center nearby for its family recreation center, the early learning day care service, and senior club. However, they are not as enthusiastic about its food bank and counseling services. You can base your evaluation proposal on a description of a program or initiative that already exists in that institution, or you can propose a different one that you are confident would be pertinent for it. Think about what information you might need to communicate to each of the four stakeholders and the best methods to accomplish this. Consider any ethical considerations that might apply to communication with stakeholders. Submit a 4-page paper that addresses the following: Identify the institution (See above description of Centennial Community Association) and write a brief (approximately 100 words) evaluation proposal for a need it may have. The goal is to be concise and yet specific. Create profiles of four stakeholders that would be involved in or affected by an evaluation at this organization. Explain the level of contact or information that each stakeholder would need before, during, and after an evaluation project as well as each stakeholder’s familiarity with evaluation and its vocabulary. Explain the optimal communication for each stakeholder (e.g., oral, written, face-to-face) and the considerations that would be best practices in any plan (e.g., reading level, linguistic diversity, physical impairments to communication). Explain any methodology issues that would be pertinent to stakeholder communication in this setting. For example, if you profile stakeholders who are clients at a hospital clinic, you might identify data collection through anonymous questionnaires rather than a Delphi technique that requires repeated contact. Finally, explain and address any ethical considerations for your communication plan with stakeholders. Please use APA style format, at least 5 APA cited references, and Time Roman 12 font.