...Last week, we found that average performance ratings do not differ between males and females in the population. Now we need to see if they differ among the grades. Is the average performace rating the same for all grades? (Assume variances are equal across the grades for this ANOVA.) You can use these columns to place grade Perf Ratings if desired. A B C D E F Null Hypothesis: Alt. Hypothesis: Place B17 in Outcome range box. Interpretation: What is the p-value: Is P-value < 0.05? Do we REJ or Not reject the null? If the null hypothesis was rejected, what is the effect size value (eta squared): Meaning of effect size measure: What does that decision mean in terms of our equal pay question: 2 While it appears that average salaries per each grade differ, we need to test this assumption. Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.) Use the input table to the right to list salaries under each grade level. Null Hypothesis: If desired, place salaries per grade in these columns Alt. Hypothesis: A B C D E F Place B55 in Outcome range box. What is the p-value: Is...
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...Last week, we found that average performance ratings do not differ between males and females in the population. Now we need to see if they differ among the grades. Is the average performace rating the same for all grades? (Assume variances are equal across the grades for this ANOVA.) You can use these columns to place grade Perf Ratings if desired. A B C D E F Null Hypothesis: Alt. Hypothesis: Place B17 in Outcome range box. Interpretation: What is the p-value: Is P-value < 0.05? Do we REJ or Not reject the null? If the null hypothesis was rejected, what is the effect size value (eta squared): Meaning of effect size measure: What does that decision mean in terms of our equal pay question: 2 While it appears that average salaries per each grade differ, we need to test this assumption. Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.) Use the input table to the right to list salaries under each grade level. Null Hypothesis: If desired, place salaries per grade in these columns Alt. Hypothesis: A B C D E F Place B55 in Outcome range box. What is the p-value: Is...
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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 C S ...
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...ft Beta Estimation Practice And Its Reliability Biasness Towards Aggressive Stocks: An Empirical Evidence From NSE * Dr. Neeraj Sanghi ** Dr. Gaurav Bansal INTRODUCTION While investing in a capital market, investors always have concern about the market movements or changes in the value of capital market index. This tendency of investors' behavior is related to a psychological factor that reveals that market movements and prices of stocks are closely related to each other. Upward / downward movement in market index gives trigger to the expectation of investors that the value of their holding would move accordingly. This is, more formally, known as systematic risk arising on account of economic wide uncertainties and explains the tendency of stock's price movement together with changes in market index. Systematic risk, also known as market risk, cannot be reduced through diversification of stocks' portfolio. Investors arc exposed to market risk even when they hold well diversified portfolio of securities. In finance literature, beta coefficient is a measurement statistic of systematic risk; it refers to the slope in a linear relationship fitted to data on the rate of return on a stoek and Ihc rate of return of the market (or market index). This usage stems from Sharpe's 1963 paper in Management Science. Beta is the stock's sensitivity to the market index: it is the degree (in percentage) by which the stock's relum lends to increase or decrease for every 1% increase or decrease...
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...1.1) Definition of 'Mode' A statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing the data in order to count the frequency of each result. The result with the highest occurrences is the mode of the set. Other related terms include the mean, or the average of a set; and the median, or the middle value in a set. Investopedia Says Investopedia explains 'Mode' For example, in the following list of numbers, 16 is the mode since it appears more times than any other number in the set: 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48 A set of numbers can have more than one mode (this is known as bimodal) if there are multiple numbers that occur with equal frequency, and more times than the others in the set. 3, 3, 3, 9, 16, 16, 16, 27, 37, 48 In this example, both the number 3 and the number 16 are modes. If no number in a set of numbers occurs more than once, that set has no mode: 3, 6, 9, 16, 27, 37, 48 Fashion is generally an answer to the question, "What is the mode?" e.g. "What's the most popular sneaker?" or "What shirt style would most people want to wear?" 1.2) Definition of 'Median' The middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be arranged in value order from lowest to highest. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above....
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...Time Series A time series is a sequence of observations which are ordered in time (or space). If observations are made on some phenomenon throughout time, it is most sensible to display the data in the order in which they arose, particularly since successive observations will probably be dependent. Time series are best displayed in a scatter plot. The series value X is plotted on the vertical axis and time t on the horizontal axis. Time is called the independent variable (in this case however, something over which you have little control). There are two kinds of time series data: Continuous, where we have an observation at every instant of time, e.g. lie detectors, electrocardiograms. We denote this using observation X at time t, X(t). Discrete, where we have an observation at (usually regularly) spaced intervals. We denote this as Xt. Examples Economics - weekly share prices, monthly profits Meteorology - daily rainfall, wind speed, temperature Sociology - crime figures (number of arrests, etc), employment figures COMPONENTS Trend Component We want to increase our understanding of a time series by picking out its main features. One of these main features is the trend component. Descriptive techniques may be extended to forecast (predict) future values. Trend is a long term movement in a time series. It is the underlying direction (an upward or downward tendency) and rate of change in a time series, when allowance has...
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...The purpose of this paper is to review the hypothesis testing of the influence bank account balances have on ATM transactions. Team A will use a two-sample hypothesis test to compare two means to examine the hypothesis. The first part of the process will develop the hypothesis statement numerically and verbally. The test begins with the determination of the level of significance and decision rule whether to accept or not reject the null hypothesis. Calculating the test statistic will provide basis of the decision according to the critical region. The final section will describe the results in relation to the research question of bank account balance influencing the number of ATM transactions. Hypotheses Team A uses a five step hypothesis testing method as part of the research for this document in determining if two sample groups of bank account balances influence the number of ATM uses in one month. As with the steps for a one population hypothesis test, a two population hypothesis test follows the same sequence. Step one for Team A starts with stating the null hypothesis. Given the data shown in Appendix A and Appendix B, Team A has a hunch that bank account holders with larger balances tend to use ATMs more frequently than low account balance holders. Group A, from Appendix A, hold balances under $1600 for a given month and the Team measures the lower balance account’s ATM transactions during the given month. Group B samples include accounts with balances...
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...Hypothesis Testing Opinions of Social Security System Probability and statistics August 1 2013 1. The Problem In an effort to design better advertising campaigns, the public relations department of the Social Security Administration conducted a survey to find out the opinions people in the United States have about the Social Security System. The public relations department collected and analyzed the survey data and claims that 40% of people in the United States think the Social Security system will have money available to provide the benefits they expect for their retirement. Also, they claim that the average age of people in the United States who would say yes to this question when asked is 60 years or older. The purpose of this study is therefore to examine and test the hypothesis of these claims and determine whether they can be supported or rejected for advertising purposes. 2. The Research Design and Hypothesis To test the hypothesis, a data table was collected from a survey adapted from Newsweek, by the public relations department of the Social Security Administration. The survey consisted of data from 32 adults ranging in age from 18 to 83. The study examines the two hypothesis by utilizing the classical method to construct a condition for testing the hypothesis claimed by the public relations department of the Social Security Administration. In this case, the null hypothesis is 40% of the people in the United States think the Social Security...
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...edu/~jdemaio/1107/hypothesis_testing.htm | | | Hypothesis TestingA statistical hypothesis is a statement about the value of a population parameter.The Alternative Hypothesis, Ha, is usually the hypothesis for which the researchers wish to gather evidence to support.The Null Hypothesis, Ho, is usually the hypothesis for which the researchers wish to gather evidence to reject. The Null Hypothesis, Ho, is always expressed in the form of an equality. i.e. Ho: = 5.8 lbs. or Ho: p= 3.2%example: The Georgia Department of Transportation claims the average number of accidents on I-285 each day is 3.2. We believe the claimed average is too small. State Ho and Ha. Ho: = 3.2Ha: > 3.2example: Kennesaw State University claims the average GPA is 2.73. We believe the claimed average is incorrect. State Ho and Ha. Ho: = 2.73Ha: 2.73A one-tailed test is one where Ha is directional and includes < or >.orA two-tailed test is one where Ha no direction is indicated and utilizes . What can go right? Decide Ho is true when it is true. Decide Ha is true when it is true. What can go wrong? Decide Ho is true when it is false. Type II errorDecide Ha is true when it is false. Type I errorThe level of significance , is the probability of making a Type I error.The rejection region is the set of possible values for which the null hypothesis will be rejected. This region will depend on .In specifying the rejection region for a hypothesis, the value at the boundary of the rejection...
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...Claim: The proportion of people using facebook is greater than 50%? Step1: State the null and alternative hypothesis. Null hypothesis: H0: That is, the proportion is less than or equal to 50% Alternate hypothesis: H1: That is, the proportion is greater than 50% Step 2: Determine the rejection regions. Select a level of significance α = 0.05 For a right-tailed test, we want the right-tail area to be α = .05. The critical value of z that accomplishes this is z.05 = 1.645. The decision rule is Reject H0 if z > 1.645 Otherwise do not reject H0 Step 3: Calculate the value of the test Statistic. Sample proportion, The value of the test statistic is Step 4: Make a decision. The value of the test statistic (2.45) is greater than the critical value of Z (1.645) and it falls in the rejection region. Hence, we reject the null hypothesis. Step 5: Conclusion. We conclude that the proportion of people using facebook is greater than 50%. Claim: Does the average children living along with them is less than 2? Step1: State the null and alternative hypothesis. Null hypothesis: H0: That is, the average children living along with them is greater than or equal to 2 Alternate hypothesis: H1: That is, the average children living along with them is less than 2 Step 2: Determine the rejection regions. The significance level is, α = 0.05 The degree of freedom is given by n-1 = 24-1=23 ...
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...Hypothesis Reflection Learning Team A: Kala Chavez, Jessica Gonani, Stacie Knauss, Michael Orcutt, and Troy Stodard QNT 351/Statistics for Business and Economics June 17, 2014 Don Silva Hypothesis Reflection This week Learning Team A is tasked with discussing three parts to hypothesis research. These objectives included evaluating the steps to test a research hypothesis, compare the means of two or more groups, and calculating the correlation between the two variables. By discussing these three objectives, team A will gain a better understanding of how the objectives are associated with statistical analysis. Research hypothesis Testing a theory or hypothesis sounds like an easy task but it is not. There are many steps to testing a research hypothesis. The five steps of hypothesis testing are (The University of North Carolina at Chapel Hill, 2012): 1. Stating the research question or questions 2. Specifying the null and alternative hypothesis involved 3. Calculating the test statistics 4. Computing the probability of test statistics or the rejection region 5. Stating the conclusions The first step, stating the research question, will clearly define and identify the research question. The population of interest, hypothesized values, and the parameters of the variables are clearly stated. Next is to state the hypothesis of at least two possible outcomes. These are the null and alternative hypothesis. The null hypothesis states that nothing will...
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...MGMT600-1501A-03 Null and Alternative Hypothesis Instructor: Professor Dr. Throop, R. February 2, 2015 Null and Alternative Hypothesis A senior executive at Company W is having an issue understanding the concept of null and alternative hypothesis in the snack food research. In this paper, I will make it understandable for him to be able to see how this hypothesis’s work. Though it may be a little cryptic, the concept of null and alternative hypothesis is not very difficult. A null hypothesis is the speculation of a declaration that researchers hope to try to nullify or disprove. The alternative hypothesis is what the researcher actually believes to be the truth about the declaration (M.U.S.E, 2015). A hypothesis involves two types of statements: the null and alternative hypothesis. Statistical implication starts by identifying that research questions can be stated in conditions of a choice between two clear and mutually options. The only reason that null hypothesis and alternative hypothesis are different is chance. Let me break this down so that it will be easier to understand. I will break it down in a formula based statement in regards to the sack food industry. Let us look at this: A researcher must present a statement that is able to be proved or disproved. Once the expectation is known, then a counter statement is provided, which also known as the “null” hypothesis. We can represent this by using the term “H0” which means: H is the hypothesis and 0 is there is no difference...
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...researching a hypothesis, compare the means of two or more groups, and calculate the correlation between two variables. In this paper, Team C will explain the steps in researching a hypothesis; illustrate a comparison between the means of two or more groups, and make a calculation of the correlation between two variables. We will also reflect on the topics in week four that we are most comfortable with and the topics we struggled with at the same time. Additionally, we will explain how the topics relate to the applications within our personal or professional fields. Steps in Research Hypothesis In science class as children we were taught that a hypothesis was an educated guess, as we blossom into a more mature age we discover that it goes a bit deeper. A hypothesis can be used in different ways most of them in our daily lives. There are two types of statistical test you can perform. The null hypothesis’s that which represents the status quo to the party performing the sampling experiment—the hypothesis that will be accepted unless the data provide convincing evidence that it is false. The alternative, or research, hypothesis is that which will be accepted only if the data provide convincing evidence of its truth. In statistic, there are seven steps you need to perform to arrive at a statistical hypothesis. The first step is the null hypothesis in which you must state a fact until it is proven to be false. The alternative hypothesis is a rejection of the null hypothesis in which...
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...Hypothesis Testing Tricia Gifford PSY/315 May 4, 2015 Karen Hoeve Hypothesis Testing Before a hypothesis test can be performed, it would be beneficial to have an understanding of what a hypothesis test is inclusive. A hypothesis is a declaration made in advance based on informal observation, a theory, or previous research, which is tested in a study. When this hypothesis declaration has been made, the hypothesis test can then be performed, which is a process for making a decision as to the outcome of a study supporting a particular theory or realistic innovation primarily thought to pertain to a population. In this hypothesis-testing scenario presented, a chosen research topic will be described along with its hypothesis statement concerning the topic. A population and its description will be determined and how the sampling method was obtained. The statistical technique will also be analyzed determining of the data. Research Issue The hypothesis test always starts out with a question regarding a subject of interest. The subject of interest is to determine if the suicide rate in the Pacific Northwest population is higher than the suicide rate in the South Midwest population. The states included in the Pacific Northwest are Idaho, Oregon, and Washington, and the states inclusive in the South Midwest are Arizona, New Mexico, and Texas. The populations are: 1) residents in the Pacific Northwest, and 2) residents in the South Midwest. With...
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...March 11, 2013 Introduction to Hypothesis Testing 1. Reminder: We have been finding probabilities related to given sample means based on given population means and standard deviations A. Example: what is the probability of finding a sample mean that is further from the population mean than this sample mean is? B. Why ask this question? - maybe this sample actually came from a population with a DIFFERENT mean - if so, we’d say the difference between our sample mean and population mean is “significant” – i.e., not due to random chance 2. Formalizing this logic… Statistical hypotheses A. The Null Hypothesis: H0 - states that there is NO difference between population means - this is like saying that any difference in sample means is due to chance - we always start by assuming this (like “innocent until proved guilty”) B. The Alternative Hypothesis: H1 - states that there IS a difference between population means - this is what we conclude when a difference is too unlikely to happen by chance C. How unlikely is TOO unlikely? - we set a cut-off point: the alpha level (α) - the alpha level marks the extreme parts of the distribution: the critical region - the critical region is usually the extreme 5% - if the sample mean is in the critical region, we reject the null hypothesis (guilty) - otherwise we accept the null hypothesis (not guilty) 3. Hypothesis testing with z-scores: scenario A. Set-up: - You know the mean and standard deviation of some population (Population A) - You also have...
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