...2 Markan Priority---------------------------------------------------------------------------------------------3 Q Hypothesis------------------------------------------------------------------------------------------------4 L and M------------------------------------------------------------------------------------------------------6 Two Gospel Hypothesis-----------------------------------------------------------------------------------7 Conclusion--------------------------------------------------------------------------------------------------10 Bibliography------------------------------------------------------------------------------------------------11 Introduction There are differences in the area of Synoptic Gospel as well as there are large amounts of similarities that can be proved with all the evidence written as well as physical. The synoptic Gospels are ones that include Matthew, Luke and Mark. The reason they are called synoptic, which means, seen together, is because of their adjacent similarities, which allow the texts to be set out in congruence for comparison. It is commonly established that there is a “literary relationship” between them, but the “phenomena” are multifaceted and rulings on them are “conflicting.” “Prevailing in modern critical scholarship is the Two Document Hypothesis (TDH), namely, that Mark was the first gospel and was one of two...
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...Synoptic Gospels, it is referred to as triple tradition. The material that is only found in Matthew and Luke is called double tradition, or Q. Also, the material that distinctively belongs to Matthew is called the M tradition, while that which belongs to Luke is called the L tradition” (The) The content of M suggests that the community for which this gospel was written, as stricter than the others in its attitude to keeping the Jewish law, holding that they must exceed the scribes and Pharisees in “righteousness (adherence to Jewish Law); and the three M refers to a church, an organized group with rules for keeping order. Biblical scholars generally hold that Matthew was composed between the years c.70 and 100” (Gospels). “Historically, two (2) basic solutions to the Synoptic Problem have...
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...LIBERTY UNIVERSITY THE SYNOPTIC PROBLEM A RESEARCH PAPER SUBMITTED TO DR. CAROL A. THOMAS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE COURST NBST 525 LIBERTY BAPTIST THEOLOGICAL SEMINARY BY LYNCHBURG, VIRGINIA , 2013 CONTENTS INTRODUCTION 1 EXPLORATION OF THE SYNOPTIC GOSPELS........................................................................1 ORAL THEORY.............................................................................................................................2 THE TWO-SOURCE HYPOTHESIS.............................................................................................3 THE GREISBACH HYPOSTHESIS..............................................................................................4 THE FARRER-GOULDER HYPOTHESIS...................................................................................5 THE AUGUSTINE HYPOSTHESIS..............................................................................................6 DEFENSE OF THE SYNOPTIC PROBLEM................................................................................6 CONCLUSION...............................................................................................................................7 BIBLIOGRAPHY...........................................................................................................................9 INTRODUCTION At first, one reads the words “Synoptic Problem” and assumes the worst. The expression...
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...Hypothesis Quality Associates, Inc. is a consulting firm that advises its clients about sampling and statistical procedures that can be used to control manufacturing processes. In one case, a client provided Quality Associates with a sample of 800 observations that were taken during a time when the client's process was operating satisfactorily. The sample standard deviation for these data was .21, hence, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows: H0: μ=12 Ha: μ≠ 12 Corrective action will be taken when H0 is rejected. Samples collected during the first day of operation of the new statistical process-control procedure are in the file Quality.xls. The URL to this dataset is A. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any should be taken, Answer H0: μ=12 Ha: μ≠ 12 Test Statistic used is Z test Decision rule: Reject null hypothesis, if the value of test statistic is greater the critical value...
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...Hypothesis Testing Statistical Method Karl Phillip R. Alcarde MBA University of Negros Occidental-Recoletos DEFINITION DEFINITION Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. The method of hypothesis testing can be summarized in four steps. 1. To begin, we identify a hypothesis or claim that we feel should be tested. For example, we might want to test the claim that the mean number of hours that children in the United States watch TV is 3 hours. 2. We select a criterion upon which we decide that the claim being tested is true or not. For example, the claim is that children watch 3 hours of TV per week. Most samples we select should have a mean close to or equal to 3 hours if the claim we are testing is true. So at what point do we decide that the discrepancy between the sample mean and 3 is so big that the claim we...
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...Hypothesis Test for a Proportion This lesson explains how to conduct a hypothesis test of a proportion, when the following conditions are met: * The sampling method is simple random sampling. * Each sample point can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. * The sample includes at least 10 successes and 10 failures. (Some texts say that 5 successes and 5 failures are enough.) * The population size is at least 10 times as big as the sample size. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa. Formulate an Analysis Plan The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements. * Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used. * Test method. Use the one-sample z-test to determine whether the hypothesized population proportion differs significantly from the observed sample proportion. Analyze Sample Data Using sample data, find the test statistic and its associated P-Value...
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...comparing two population means with an unknown standard deviation you use a t test and you use N-2 degrees of freedom. A. True | B. False | | Reset Selection Question 2 of 20 | 5.0 Points | Pretend you want to determine whether the mean weekly sales of soup are the same when the soup is the featured item and when it is a normal item on the menu. When it is the featured item the sample mean is 66 and the population standard deviation is 3 with a sample size of 23. When it is a normal item the sample mean is 53 with a population standard deviation of 4 and a sample size of 7. Given this information we could use a t test for two independent means. A. True | B. False | | Reset Selection Question 3 of 20 | 5.0 Points | The alternative hypothesis can be proven if the alternative hypothesis is rejected. A. True | B. False | | Reset Selection Question 4 of 20 | 5.0 Points | You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 50 and a population standard deviation 5 and a sample size of 100. Machine 2 has a sample mean of 52 and a population standard deviation of 6 with a sample size of 36. With an alpha of .10 can we claim that there is a difference between the output of the two machines. Which of the following statements are true? A. We will reject the null hypothesis and prove there is a difference between the 2 populations | | B. We will not reject the null hypothesis and thus...
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...CHAPTER 9 Hypothesis Tests CONTENTS 9.4 POPULATION MEAN: σ UNKNOWN One-Tailed Test Two-Tailed Test Summary and Practical Advice 9.5 POPULATION PROPORTION Summary 9.6 HYPOTHESIS TESTING AND DECISION MAKING 9.7 CALCULATING THE PROBABILITY OF TYPE II ERRORS 9.8 DETERMINING THE SAMPLE SIZE FOR A HYPOTHESIS TEST ABOUT A POPULATION MEAN STATISTICS IN PRACTICE: JOHN MORRELL & COMPANY 9.1 DEVELOPING NULL AND ALTERNATIVE HYPOTHESES The Alternative Hypothesis as a Research Hypothesis The Null Hypothesis as an Assumption to Be Challenged Summary of Forms for Null and Alternative Hypotheses 9.2 TYPE I AND TYPE II ERRORS 9.3 POPULATION MEAN: σ KNOWN One-Tailed Test Two-Tailed Test Summary and Practical Advice Relationship Between Interval Estimation and Hypothesis Testing 349 Statistics in Practice STATISTICS in PRACTICE JOHN MORRELL & COMPANY* CINCINNATI, OHIO John Morrell & Company, which began in England in 1827, is considered the oldest continuously operating meat manufacturer in the United States. It is a wholly owned and independently managed subsidiary of Smithfield Foods, Smithfield, Virginia. John Morrell & Company offers an extensive product line of processed meats and fresh pork to consumers under 13 regional brands including John Morrell, E-Z-Cut, Tobin’s First Prize, Dinner Bell, Hunter, Kretschmar, Rath, Rodeo, Shenson, Farmers Hickory Brand, Iowa Quality, and Peyton’s. Each regional brand enjoys high brand recognition and loyalty among consumers. Market...
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...Hypothesis Testing: One Population Hypothesis testing is used to make decisions about a population based on the analysis of sample statistics. There are always two hypothesis statements which are mutually exclusive and complementary statements concerning the value of the population parameter of interest: Null Hypothesis (H0): An assumption regarding a population parameter of interest. This hypothesis always includes the equal sign as the null hypothesis is assumed to be true unless sample data produces evidence to the contrary. Alternative Hypothesis (H1): The alternative option available when the null hypothesis is rejected. Three Types of Hypothesis Tests: Lower-Tail Test Upper-Tail Test Two-Tailed Test H0: ( ( (0 H0: ( ( (0 H0: ( = (0 H1: ( < (0 H1: ( > (0 H1: ( ( (0 Two-Sided Tests: A Two-Tailed Test (TTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some different value. One-Sided Tests: A Lower-Tail Test (LTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some lower value. An Upper-Tail Test (UTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some greater value. Test Statistics and Action Limits: A test statistic is a sample statistic corresponding to the population parameter being tested. For example, when testing a hypothesis...
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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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...Applied Business Statistics FINAL Examination 1. The t distribution A) assumes the population is normally distributed. B) approaches the normal distribution as the sample size increases. C) has more area in the tails than does the normal distribution. D) All of the above. 2. Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" in an inference. A) In repeated sampling, the population parameter would fall in the given interval 95% of the time. B) In repeated sampling, 95% of the intervals constructed would contain the population mean. C) 95% of the observations in the entire population fall in the given interval. D) 95% of the observations in the sample fall in the given interval. 3. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a wider interval. A) narrower B) wider C) less significant D) biased 4. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income? A) $15,052 B) $15,141 See worksheet C) $15,330 D) $15,364 5. A prison official wants to estimate the proportion of cases of recidivism....
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...the sample. It helps him decide whether to accept or eject a hypothesis after evaluating the sample. Statistical hypothesis Hypothesis is a theory, claim or assertion about a particular parameter of a population. It needs to be proven true. Once proven true, it is accepted; otherwise, it is rejected. Types of hypothesis: 1. Null hypothesis (Ho) is always one of status quo or no difference. Example: Ho : The mean fill per box of cereal is 368 grams. (μ = 368) 2. Alternative hypothesis (H1) is the opposite of the null hypothesis (Ho). it is the statement of difference Example: H1: The mean fill per box is not 368 grams. (μ ≠ 368) A summary of the null and alternative hypothesis is presented below: The following two key points summarize the null and alternative hypothesis: 1. The null hypothesis Ho is the hypothesis that is always tested. 2. The alternative hypothesis h1 is set up as the opposite of the null hypothesis and represents the conclusion supported if the null hypothesis is rejected. In what is known as classical hypothesis-testing methodology, we have the following three key points: 1. The null hypothesis Ho always refers to a specified value of the population parameter (such as μ), not a sample statistic (such as X) 2. The statement of the null hypothesis always contains an equal sign regarding the specified value of the population parameter (i.e. H0 = 368 grams) 3. The statement of the alternative hypothesis never...
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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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...Bahria University Bahria Institute of Management & Computer Sciences Karachi Campus Course Title: Statistical Inference Course Code: QTM 220 Credit Hours: Three Semester: 3rd Semester Prerequisite: QTM 160 Aims and Objectives: This main objective of this course is to provide wide application f the statistical tools in business management. It is also aims at to impart in-depth and rigorous knowledge to the business students to inculcate academic excellence in various fields of research and development, with special reference to business management. In addition it will provide necessary statistical knowledge and wide rage of ways to analyze data, which will improve the students statistical analytical and decision making skills. Session Lecture Outline Learning Objectives 01 Basic Probability and Discrete Probability Distributions Simple Probability To develop an understanding of basic probability concepts To introduce conditional probability To use Bayes’ Theorem to revise probabilities in light of new information To provide an understanding of the basic concepts of discrete probability distributions and their characteristics To develop the concept of mathematical expectation for a discrete random variable To introduce the covariance and illustrate its application in finance To present applications of the binomial distribution in business To present applications of the Poisson distribution in business 02 Counting Techniques 03 Continued...
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...11-list the five steps of hypothesis testing and explain the procedure and logic of each. Step 1: Restate the question as a Research Hypothesis and a Null Hypothesis about the populations (Aron, 2009). We want to put this into clear terms with our population 1 in the first group stating what our opinion of the research is, why we are performing the research, and what we feel the outcome will be. We then state a null hypothesis to make clear we understand there is an alternative. That is, our prediction may not be correct, there may be no effect. This is considered population 2. Step 2: Determine the characteristics of the Comparison Distribution (Aron, 2009). We want to determine if the null hypothesis is true, what is the situation that makes it so. We want to state that the population 1 is not the normal curve and population 2 is. If the null is true, they will both follow the normal curve. We will compare the two scores of the test to examine our results and to test the hypothesis and the null against one another. Step 3: Determine the Cutoff Sample Score on the Comparison Distribution at which the Null Hypothesis should be rejected (Aron, 2009). Before our initial test, we will determine a score of which our results will be compared. We need evidence to prove that our hypothesis is true and the null is not. The significance level is the probability of making a Type I error. This occurs when the decision supports the alternative hypothesis when the null is true. A...
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