2020, OPMT-600LESSON 91Lesson 9: Binomial Distribution to Think DistributionallyDiscovery consists of looking at the same thing as everyone else and thinking something different.Albert Szent-GyörgyiThe following link is to a video that discusses the binomial distribution: Introduction to the Binomial DistributionQuestion 1: The answers to Question 1 are at the end of the lesson. DO NOT TURN IN QUESTION 1. I encourage you to answer the questions and check yourself.A for profit survey research company is hired by a non-partisan television network news to project whether candidate A or B will win a U.S. Senate election.a)Phase I: What is the goal of the research company?b)Discuss whythey are doing the study by looking at the consequences to the research company of making an alpha error and beta error assuming: B A will win the election O B B will win the electionc)Phase II: What assumptionswould the research company make to justify using Inductive Reasoning?d)Phase III: What would they measureto achieve their goal (Phase I)
2020, OPMT-600LESSON 92e)Phase IV: Discuss who they will selectto measure; clearly define the population of interest and the Sampling Methodology used.f)Phase V how they will measure: Discuss the issues of accuracy, reliability and precision remembering we have stipulated definitions for each of these terms.g)Assume that in reality 45% favor A and 55% favor B, what is the probability that 11 or more of the 20 voters in the survey will favor A? Hint: Use Binomial Distribution - Excel or any stats package or tables in the book, you should get an answer of approximately 25%. Remember, P(x≥11) = 1-P(x≤10).h)Same problem as a) above, but now a survey of 100 voters is taken and you want to determine the probability that 51 or more of the 100 voters will favor A. You should get an answer of approximately 13%.i)Explain why the probabilities determined in questions g) and h) are important to the survey research company. Think about how the information from the survey will be usedto project the winner. Hint: survey research companies attempt to quantify the risk of sampling errors (aand berrors).j) The probabilities in g) and h) are different; what basic statistical concept is this differencedemonstrating?
2020, OPMT-600LESSON 93Question 2:Currently an herbal salve sold over the counter is used to treat an annoying rash; no major health issues, the patient simply has green dots on their entire body. The herbal salve has beenused for years, so its effectiveness is well established. Sixty percent of the patients reported thegreen dots disappeared, after using the herbal salve.A new salve claiming to be more effective and selling at the same price as the herbal salve has just been introduced and sold over the counter. As a dermatologist you want to determine if the new salve is better. You have time to test the new salve on 15 patients and want to be at least 90% confident of your decision to use the new salve.