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Hypothesis Testing Assignment 1 Solution

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Hypothesis Testing

Welcome to Week Five, Module Five Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected The null hypothesis, denoted by H0 , is a tentative assumption about a population parameter. The alternative hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis The hypothesis testing procedure uses data from a sample to test the two competing statements indicated by H0 and Ha. Researchers Investigate Many Types of Questions Accountant: evidence exists for corporate tax fraud. Department of Homeland Security: test whether a new surveillance method will uncover terrorist activity. Sociologist: examine whether the mayor’s economic policy is increasing poverty in the city. Questions such as these can be tackled using Statistical hypothesis testing. Basic idea of hypothesis testing: Make a decision about the value of a population parameter (such as μ or p). True value of parameter unknown. May be different hypotheses about the true value of this parameter. Table 1 The three possible forms for the hypotheses A picture containing tableDescription automatically generated Recall that each hypothesis is a claim that the statement is true. Find evidence that is consistent with one of the two claims H0 or Ha. The first task in hypothesis testing is to form hypotheses. Table 1 Key English words, with mathematical symbols and synonyms. Strategy for Constructing the Hypotheses About μ Step 1 : Search problem for keywords using Table 2. Step 2: Determine form of hypotheses using Table 1. Step 3: Find value of μ0 (the number that answers the question: “Greater than what?” or “Less than what?”) and write hypotheses. Null Hypothesis as an Assumption to be Challenged We might begin with a belief or assumption that a statement about the value of a population parameter is true We then use a hypothesis test to challenge the assumption and determine if there is statistical evidence to conclude that the assumption is incorrect In these situations, it is helpful to develop the null hypothesis first Example: The label on a soft drink bottle states that it contains 67.6 fluid ounces Null Hypothesis: The label is correct. μ > μ0 H0 : μ > 67.6 ounces. Alternative Hypothesis: The label is incorrect. μ < μ0 Ha : μ < 67.6 ounces Type I and Type II Errors Example In the United States, a defendant is innocent until proven guilty. Jury must evaluate the truth of two competing hypotheses: H0: defendant is not guilty vs. Ha: defendant is guilty Four possible outcomes tb0903 The Essential Idea About Hypothesis Testing for the Mean If observed value of x is unusual or extreme in the sampling distribution of x when assuming H0 is correct, reject H0. Otherwise, there is insufficient evidence against H0, and do not reject H0. p-Value Probability of observing a sample statistic (such as x or Zdata) at least as extreme as observed statistic assuming null hypothesis is true. Roughly speaking, represents probability of observing sample statistic if the null hypothesis is true. Since term “p-value” means “probability value,” always lies between 0 and 1. Finding the p-value depends on the form of the hypothesis test. I hope everyone will have a wonderful productive week, do not hesitate to contact me for questions or concerns. References: Textbook: Discovering Statistics- Brief Version, by Daniel Larose, 1st edition, by W.H. Freeman and Company, New York. Textbook: David R. Anderson, Statistics for Business & Economics: Selected Chapters, 13th Edition, Cengage Learning, 2016. Zybooks : 5.1 Hypothesis testing https://learn.zybooks.com/zybook/SNHUMAT240Master1/chapter/5/section/1 Zybooks : 5.2Hypothesis test for a population mean https://learn.zybooks.com/zybook/SNHUMAT240Master1/chapter/5/section/2 Week Four/ Module Four Sep 19, 2021 4:05 PM Hello All, We are almost halfway through the term, and it looks great. Please finish all activities, and assignments for previous modules, I’m doing my best with late penalties. Module four with regular activities, it contains our first project, please do not forget to do, and submit project one. Welcome to Module Four. Uncertainties Managers often base their decisions on an analysis of uncertainties such as the following: What are the chances that sales will decrease if we increase prices? What is the likelihood a new assembly method will increase productivity? What are the odds that a new investment will be profitable? Probability is a numerical measure of the likelihood that an event will occur. Probability values are always assigned on a scale from 0 to 1. A probability near zero indicates an event is quite unlikely to occur. A probability near one indicates an event is almost certain to occur. Continuous Probability Distributions Uniform Probability Distribution A probability density function (pdf) describes the relative likelihood of all values for a continuous random variable A cumulative distribution function (cdf) of a continuous random variable x is the probability that for any number

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