...M&M Project Math 336 (1) Buy a packet of regular size M&M's. Record the frequency of each color and then transfer this information to a bar chart and a pie chart. (2) Represent the number of M&M's per packet on a histogram using all of the class data. Is your histogram normally distributed? Check using the empirical rule. Also choose your favorite color and draw a histogram of the number of M&M’s of that color per packet based on class data. Draw a box-plot of the total number of data in a packet based on class data. (3) There are numerous hypothesis tests that can be done. Obtain the mean number of M&M's per packet for the whole class. Consider as a null hypothesize that the actual number of M&M's in your packet is the actual number of M&M's per packet as intended by the manufacturers. Test this hypothesis using the sample data from the class. Comment on the difference between a type I and type II error in this context. (NOTE: Be careful in the choice of your sample size.) (4) Test the assumption that on average there are the same proportion of red and yellow M&M’s per packet. (5) Devise a test to see if there are the same number of red M&M’s per packet. (6) Another obvious test would be to test the proportion of colors present. Intuitively, we might expect each color to occur with the same probability p (Null Hypothesis) but a quick inspection of data suggests this is not so. Test this hypothesis. (5) Perhaps the manufacturers do not stick to any...
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...Introduction to Hypothesis Testing 8.1 8.2 8.3 8.4 8.5 CHAPTER 8 Inferential Statistics and Hypothesis Testing Four Steps to Hypothesis Testing Hypothesis Testing and Sampling Distributions Making a Decision: Types of Error Testing a Research Hypothesis: Examples Using the z Test Research in Focus: Directional Versus Nondirectional Tests Measuring the Size of an Effect: Cohen’s d Effect Size, Power, and Sample Size Additional Factors That Increase Power LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 2 Identify the four steps of hypothesis testing. Define null hypothesis, alternative hypothesis, level of significance, test statistic, p value, and statistical significance. Define Type I error and Type II error, and identify the type of error that researchers control. Calculate the one-independent sample z test and interpret the results. Distinguish between a one-tailed and two-tailed test, and explain why a Type III error is possible only with one-tailed tests. Explain what effect size measures and compute a Cohen’s d for the one-independent sample z test. Define power and identify six factors that influence power. Summarize the results of a one-independent sample z test in American Psychological Association (APA) format. 8.6 3 4 5 8.7 8.8 8.9 8.10 SPSS in Focus: A Preview for Chapters 9 to 18 8.11 APA in Focus: Reporting the Test Statistic and Effect Size 6 7 8 2 PART III: PROBABILITY AND THE FOUNDATIONS OF INFERENTIAL STATISTICS 8.1 INFERENTIAL...
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...M Project Report Israel Sharipo September 13, 2013 Abstract This paper shows the true proportions of M&M candies through the random sampling of 3 different bags of plain M&M 1.69oz bag of candy bought from three different stores. I believed one will be able to determine data analysis and how it works as it relates to our class project. Introduction The rationale of writing this paper is to show how statistics data analysis works. Statistics as we learned, is the practice of collecting, organizing, analyzing and interpreting data to make decisions. The two types of data used in the project are sampling and proportions. The methods used can be used by any professional or in any occupation. It can be used to determine the standard deviation, mean of any data among others. Part 1 In part one, each student was asked to take a tally of the 3 bags of candies bought from three different stores. And then we were asked to count the totals of each color in all 3 bags. Part 2 We used the excel data provided to complete the assignment. We looked at the data from two perspectives” color and proportions and the number of candies per bag. For the color proportion; we used the total for each color divided but the total number of candies sampled. As for the number of candies per bag, we use the data in the number candies in bag column. We used the...
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...beer drinkers “could not distinguish the taste difference among the brands on an overall basis” (Allison&Uhl, 1964, p.37), moreover did the study conducted by Allison and Uhl highlight that beer drinkers were not able to identify their favorite brand of beer in a blind beer comparison test. Another study conducted by Plassmann, O’Doherty, Shiv and Rangel about how “ Marketing actions can modulate neural representations of experienced pleasantness” also identified that when participants are not presented with any particular information about the wines they had to taste in their blind test, participants were not able to report any major “differences among the wines”. (Plassmann et. All., 2007, p. 1051) Based on these findings the first hypothesis of the study is (1) Participants tested in the blind test will taste no major difference among the different coke sorts. Based on the same study about beer brand identification on taste perception, the researchers observed that participants have a certain loyalty to their preferred brands. This was highlighted when preferences for brands with higher brand equity increased when the beer brands were labeled in the study. The study of Plassmann et. Al., also provided...
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... Observe that the sample proportion is This corresponds to a two-tailed z-test for proportions. The z-statistics is computed by the following formula: The critical value for for this two-tailed test is. The rejection region is given by Since, then we reject the null hypothesis H0. Hence, we have enough evidence to reject the claim that the true proportion of blue M&Ms® candies is 0.24. 3 pts. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05 significance level. Solution: We are interested in testing the following null and alternative hypotheses We need to use the z-statistic, which is calculated using Observe that the sample proportion is This corresponds to a two-tailed z-test for proportions. The z-statistics is given by the following formula: The critical value for for this two-tailed test is. The rejection region is given by Since, then we reject the null hypothesis H0. Hence, we have enough evidence to reject the claim that the true proportion of orange M&Ms® candies is 0.20. 3 pts. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05 significance level. Solution: We want to test the following null and alternative hypotheses We need to use the z-statistic, which is computed using Observe that the sample proportion is This corresponds to a two-tailed z-test...
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...A hypothesis is a conjecture about a population. Typically, these hypotheses will be stated in terms of a parameter. A test of hypothesis is a statistical procedure used to make a decision about the conjectured value of a parameter. We will make our decision based on observed values of a statistic. * The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief about a parameter. * There are two hypotheses which we are comparing. * The null hypothesis, H0, specifies a value of a parameter. This hypothesis is assumed to be true, and the collected data will be analyzed to see if it is contradictory to the null hypothesis. * The alternative hypothesis, Ha, gives an opposing statement about the value of the parameter. The collected data will be analyzed to see if it supports the alternative hypothesis. Example: * An operation manager needs to determine if the mean demand during lead time is greater than 350. * If so, changes in the ordering policy are needed. There are two hypotheses about a population mean: * H0: The null hypothesis m = 350 * Ha: The alternative hypothesis m > 350 Decision Rule: This tells us when we feel the observed data provided sufficient evident to conclude the alternative hypothesis is true. It will be phrased as: Accept the alternative hypothesis when the p-value of the test is less than a. Steps of the Test...
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...“When the price of a stock can be influenced by a “herd” on Wall Street with prices set at the margin by the most emotional person, or the greediest person, or the most depressed person, it is hard to argue that the market always prices rationally. In fact, market prices are frequently nonsensical.” ------------------------------------------------- This report will analysis the statement by Warren Buffett, and it considers the contrasting evidence on the validity of the observation on the Efficient Markets Hypothesis. The report briefly outlines the forms of the Efficient Market Hypothesis, the report also analysis’s the evidence both seminal and recent on the theory relating to the three forms of the hypothesis. It also examines the theoretical role and motivation of analysts in creating market efficiency; lastly it looks at alternative perspectives on the pricing of securities. Introduction In 1984 Warren Buffett penned an article titled “The Superinvestors of Graham-and-Doddsville”, based on a speech he had given on the occasion of the 50th anniversary of his mentor Ben Graham’s legendary textbook, Security Analysis. In it, Buffett rejected the then growing (and now entrenched) view in academia that markets are ''efficient'' because ''stock prices reflect everything that is known about a company’s prospects and about the state of the economy.'' Warren Buffett argued against EMH, saying the preponderance of value investors among the world's best money managers rebuts...
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...Hypothes9 9.1 Fundamentals of Hypothesis Testing: One-Sample Tests A Connection Between Confidence Interval Estimation and Hypothesis Testing Can You Ever Know the Population Standard Deviation? USING STATISTICS @ Oxford Cereals, Part II Fundamentals of Hypothesis-Testing Methodology The Null and Alternative Hypotheses The Critical Value of the Test Statistic Regions of Rejection and Nonrejection Risks in Decision Making Using Hypothesis Testing Hypothesis Testing Using the Critical Value Approach Hypothesis Testing Using the p-Value Approach 9.4 Z Test of Hypothesis for the Proportion The Critical Value Approach The p-Value Approach Potential HypothesisTesting Pitfalls and Ethical Issues 9.5 9.2 t Test of Hypothesis for the Mean (S Unknown) The Critical Value Approach The p-Value Approach Checking the Normality Assumption One-Tail Tests The Critical Value Approach The p-Value Approach 9.6 Online Topic: The Power of a Test USING STATISTICS @ Oxford Cereals, Part II Revisited CHAPTER 9 EXCEL GUIDE CHAPTER 9 MINITAB GUIDE 9.3 Learning Objectives In this chapter, you learn: • The basic principles of hypothesis testing • How to use hypothesis testing to test a mean or proportion • The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are seriously violated • How to avoid the pitfalls involved in hypothesis testing • Ethical issues involved in hypothesis testing U S I N G S TAT I S T I...
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...utilizes human capital theory to model M&A events as transactions that simultaneously have cross-level, real effects on workers, plants and firms, while the traditionally method just concentrates on firm level financial performance. After the empirical studies of M&A, the author gives us a conclusion that even though M&A decreases the size of establishments and firms, it increases productivity of plant and performance of firm does not change as well. Terminologies Mergers and Acquisitions: Mergers mean that the company merged two or more independent enterprises to form a new one company. It usually consists of a dominant company to absorb one or several companies. Acquisitions mean that a business with cash or marketable securities to buy another company 's stock or assets in order to obtain title to all assets of the enterprise or the control of the enterprise. Human Capital: Measure the economic value of employees' skills set. On the basis of this measure, all of the labor is considered equal basic production inputs of labor measures. A bad match: Even though a worker is not productive enough to permit compensation, he will get the common wage, which is same as the same industry. Information asymmetry Information asymmetry refers that one party in a transaction has more information than others. Major Findings or Arguments: 1. From the Figure 1, Hypothesis one is approved. It claims that workers who work at M&A plant will get higher compensation...
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...there the scientists observation of the world as it leads to the hypothetical theory (a theory that lacks merit) This is the first step of scientific method and can be presented in two ways either as a natural observation or a staged one, Second in the collection of data in a experiment using the scientific method there are two observations ,Qualitive and Quantive. The third step to scientific method is the hypothesis (a proposed explanation for a phenomenon) for a hypothesis to be scientific hypothesis; the scientific method requires that one can test it. 4. The fourth step to scientific method is the experiment to test an hypothesis. The experiment must be unbiased in nature meaning that scientists cannot create an experiment that will favor the outcome that they predicted in their hypothesis 5. The fifth and final step in scientific method is to draw a conclusion. Scientists draw conclusions by examining the data from an experiment and there are two outcomes. Either the experiment supported the hypothesis and can be regarded as true, or the experiment disproved the hypothesis as false. The difference between science and technology are that where science is a systematically knowledge base where a series of steps is followed in order to reliably predict the type of...
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...Interpretation: An observation yij is given by: the average height of the plants (µ), plus the effect of the fertilizer (Ai ). and an ”error” term ( ij ), i.e. every seed is different and therefore any plant will be different. All these values (µ, Ai , ij ) are UNKNOWN! Our GOAL is to test if the hypothesis A1 = A2 = A3 = 0 is plausible1 . Remark 1 If we have a control group (for example treatment ”X” is ”without any fertilizer”, then we assume that the values of X are in some way the best approximation for µ, therefore we can choose A1 = 0 is spite of condition (0.2). STEP 1: complete the first table. For the treatment means it is enough to calculate the mean of the values M eanX M eanY M eanZ 1 = = = 1+2+2 = 1.667 3 5+6+5 = 5.333 3 1+2 = 1.5 2 We DO NOT find ”the correct value” for the Ai We WILL NOT find which factor (treatment) has an effect, we just look if in general treatments has effect on the results. 1 The (estimated) overall mean (ˆ, which is an estimation of the exact, unµ known overall mean µ) is calculated as follows2 : µ = ˆ 1+2+2+5+6+5+2+1 =3 8 ˆ The estimated effects Ai are the difference between the ”estimated treatment mean” and the ”estimated overall mean”, i.e. ˆ Ai = M eani − µ ˆ So ˆ A1 = 1.667 − 3 = −1.333 ˆ A2 = 5.333 − 3 = 2.333 ˆ A3 = 1.5 − 3 = −1.5 Then: Treatment X Y Z Overall mean STEP 2: The ANOVA table. Cause of the variation Treatment Residuals Total F Krit ... Measures Mean 1 2 2 1.667 5 6 5 5.333 2 1 1.5 // 3 ˆ Ai -1.333 2.333 -1.5 df...
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...M&Ms® Project Report Rachel Carr Professor Patty Fuller MAT 300- Statistics June 8, 2013 Abstract This paper is about the color proportion of each bag of M&Ms®. Now even though the factory has a claim of the each bag being grouped off into a certain percentage of each color, the results are not always the same. In fact, I will show through random selection process that M&Ms® brand candies each have a different number of candies in the bag and from that a different percentage of each color represented. I will use different statistical formulas and hypotheses to state my claim and give evidence as it relates to the results of the claim. This study was conducted in 5 different parts, by a total of 74 people, each person obtaining bags of M&Ms® in the same manner but in different locations. Title The purpose of this report is to examine the packaging process for plain 1.69 ounce bags of M&Ms®. . Part 1 For the first part of this project I went to three different stores, (Publix, Piggly Wiggly, and Trinity Gift Shop) and purchased a bag of plain 1.69oz M&Ms® at each store. Purchasing a single bag at a random store assured the process of obtaining a true random sample. After purchasing each bag of M&Ms®, I separated each bag by color and charted the results into an Excel spreadsheet: | Blue | Orange | Green | Yellow | Red | Brown | Num. of Candies in Bag | bag 1 | 2 | 14 | 12 | 8 | 10 | 11 | 57 | bag 2 | 7 | 20 | 7 | 7 | 9 | 9...
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...statistical procedures that can be used to control their manufacturing processes. The data required for the study giving to QA from the client, a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation was 0.21 and population standard deviation was assumed to be 0.21. QA suggested taking random samples of size 30 occasionally to monitor the process on an ongoing basis. The client could quickly learn whether the process was operation reasonably and if not, corrective action could be taken to remove the problem. The design specification indicated the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows. H0: u = 12 H1: u ≠ 12 Corrective action will be taken any time H0 is rejected. Conducting the hypothesis test for each sample The population of interest is 800 and each of four samples, each of size 30, collected at hourly intervals during the first day of operation of the new statistical control procedure. The two tables below shows the output of one-sample statistics test that shows the...
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...Evidence Husam-Aldin Nizar Al-Malkawi Corresponding Author, Faculty of Business, ALHOSN University P.O. Box 38772 - Abu Dhabi, UAE E-mail: h.almalkawi@alhosnu.ae Michael Rafferty Senior Research Analyst, WRC, University of Sydney, Australia E-mail: m.rafferty@econ.usyd.edu.au Rekha Pillai Faculty of Business, ALHOSN University, Abu Dhabi, UAE E-mail: r.pillai@alhosnu.ae Abstract The literature on dividend policy has produced a large body of theoretical and empirical research, especially following the publication of the dividend irrelevance hypothesis of Miller and Modigliani (1961). No general consensus has yet emerged after several decades of investigation, and scholars can often disagree even about the same empirical evidence. This paper aims at providing the reader with a comprehensive understanding of dividends and dividend policy by reviewing the main theories and explanations of dividend policy including dividend irrelevance hypothesis of Miller and Modigliani, bird-in-the-hand, tax-preference, clientele effects, signalling, and agency costs hypotheses. The paper also attempts to present the main empirical studies on corporate dividend policy. However, due to the enduring nature and extensive range of the debate about dividend policy which has spawned a vast amount of literature that grows by the day, a full review of all debates is not feasible. The paper reaches at a conclusion that the famous statement of Fisher Black about dividend policy "the harder we look at the dividends...
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...the lights on and off is they wish. After a month in the room, each individual tended to develop a study cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25. Using the 0 .5 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycling under these conditions differ significantly from 24-hour?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved, (c) explain yourself to someone who has never had a course in statistics. (a) Steps of hypothesis testing 1. Restate the question as a research hypothesis and a null hypothesis about the populations. There are two populations Population 1: people who are given the experimental test for 24 hours is the natural cycle. Population 2: people who are given the experimental test in less than 24 hours is the natural cycle. The null hypothesis: µ = 24 The alternative hypothesis: µ ≠ 24 2. Define the features of the compared distribution Sample mean: 25 M = (∑X)/N = 200/8 = 25 Sample Standard deviation: 1.195229 SD √ SD^2 = Find the estimated population variance. You first need to figure the sample mean, which is (25+27+25+ 23+24+25+26+ 25)/8 = 200/8 = 25. The estimated variance population is S^2 = SS/(N-1) = [( 25-25)^2 + ( 27-25)^2 + (25-25)^2 + (23-25)^2 + (24-25)^2 + (25-25)^2 +...
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