...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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...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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...Salaaka Reflection “The hypothesis guides us on the selection of a certain design, observation and methods of researching over others. If we could test the whole populations directly, we would not need to formulate hypothesis, conduct inferential statistics and make inferences for the population based on a sample. However, it is often impossible to test the whole population, and we need to make our observations based on a sample (University of Strathclyde Humanities & Social Studies, n.d.).” “Hypothesis testing is all about populations and using a sample based in which we make inferences about the population” (University of Strathclyde Humanities & Social Studies, n.d.). The basic logic is to prove or disprove the research question. There are five steps that consist of all the decisions a researchers needs to make in order to answer any research question. Steps in Testing a Research Hypothesis 1. Stating the Research Question. “This step makes the researcher not only define what is to be tested but what variable will be used in sample data collection” ("Five Steps of Hypothesis Testing", 2014). 2. Specify the Null and Alternative Hypothesis – According to the University of North Carolina (2014), "The second step is to state the research question in terms of a null hypothesis (H0) and a alternative hypothesis (HA). The null hypothesis is the population parameter, µ = $30,000 (H0: µ = $30,000). The alternative hypothesis is the population parameter...
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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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...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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...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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...Contents CHAPTER 9: HYPOTHESIS TESTS 9.1 Elements of a Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Normal Hypothesis Test for Population Proportion p . . . . . . . . . . . . . . . . . . 9.3 The t-Test: Hypothesis Testing for Population Mean µ . . . . . . . . . . . . . . . . . 9.4 Possible Errors in Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Limitations and Common Misinterpretations of Hypothesis Testing . . . . . . . . . . 1 1 6 10 15 17 Stat 3011 Chapter 9 CHAPTER 9: HYPOTHESIS TESTS Motivating Example A diet pill company advertises that at least 75% of its customers lose 10 pounds or more within 2 weeks. You suspect the company of falsely advertising the benefits of taking their pills. Suppose you take a sample of 100 product users and find that only 5% have lost at least 10 pounds. Is this enough to prove your claim? What about if 72% had lost at least 10 pounds? Goal: 9.1 Elements of a Hypothesis Test 1. Assumptions 2. Hypotheses Each hypothesis test has two hypotheses about the population: Null Hypothesis (H0 ): Alternative Hypothesis (Ha ): 1 Stat 3011 Chapter 9 Diet Pill Example: Let p = true proportion of diet pill customers that lose at least 10 pounds. State the null and alternative hypotheses for the diet pill example. 3. Test Statistic Definition: Test Statistic A test statistic is a measure of how compatible the data is with the null hypothesis. The larger the test...
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...One-Sample Tests of Hypothesis LEARNING OBJECTIVES 1 Define a hypothesis. 2 Explain the five-step hypothesis-testing procedure. 3 Define Type I and Type II errors. 4 Define the term test statistic and explain how it is used. 5 Distinguish between a one-tailed and a two-tailed hypothesis. 6 Conduct a test of hypothesis about a population mean. 7 Compute and interpret a p-value. 8 Conduct a test of hypothesis about a population proportion. 10-2 Define a hypothesis. Explain the five-step hypothesis-testing procedure. Hypothesis and Hypothesis Testing HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing. HYPOTHESIS TESTING A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. 10-3 The Null and Alternate Hypotheses NULL HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing numerical evidence. ALTERNATE HYPOTHESIS A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false. 10-4 Important Things to Remember about H0 and H1 H0: null hypothesis and H1: alternate hypothesis. H0 and H1 are mutually exclusive and collectively exhaustive. H0 is always presumed to be true. H1 has the burden of proof. A random sample (n) is used to “reject H0”. If we conclude “do not reject H0”, this does not necessarily ...
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... | |[pic] | |[pic] | |Alternate hypothesis |The conclusion we accept when we demonstrate that the null hypothesis is false. It is also called the | | |research hypothesis. | |[pic] | |[pic] | |[pic] | |Critical value |A value that is the dividing point between the region where the null hypothesis is not rejected and the | | |region where it is rejected. | |[pic]...
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...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 contains an equal sign regarding...
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...Nonparametric Hypothesis Testing RES/342 Nonparametric Hypothesis Testing During the course of the last three weeks, the team explored the hypothesis testing segment of statistics research. The first part of this assignment was the one sample hypothesis testing. The second was the two or more sample hypothesis testing, and finally in this third week, we will look at nonparametric hypothesis testing. This week’s project is a continuation of the previous projects and entails to build on the identical research question that we will frame a research hypothesis from the same provided data sets (Wage and Wage Earners) using ratio or interval numerical data; however, this week we will use a nonparametric hypothesis test to find our answer. In the next following paragraphs, the team will clearly affirm a hypothesis statement that will provide the base for our survey, perform a five-step hypothesis test on information concerning our choice and apply the concepts of nonparametric testing learned in this course, and describe how the results of our findings answer our research question. Finally, we will conclude this study with a brief summary that will examine the main points, the purpose, and conclusions of this final third week’s study on nonparametric testing. Perform the five-step hypothesis test on the data Nonparametric tests are statistical tests that analyze data that does not require assumptions about the distribution of shape of the population from which...
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...Applied Managerial Decision Making Phase 3 Discussion Board 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...
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...The steps in testing a research hypothesis There are a total of five steps that are used in testing a hypothesis and they are: “(1) Making assumptions, (2) Stating the research and null hypotheses and selecting (setting) alpha, (3) Selecting the sampling distribution and specifying the test statistic, (4) Computing the test statistic, and (5) Making a decision and interpreting the results.” (Boston University Metropolitan College, n.d., Para. 1). When beginning the process of creating a hypothesis to test, the first thing that must be done is to make assumptions about the type of sampling method that would be used, the level of measurement for the variable, including the sample size. The second step is then to state the research and null hypotheses and selecting the alpha. “We always state research hypotheses in terms of population parameters because we want to use sample statistics to estimate population parameters.” (Boston University Metropolitan College, n.d., Para. 5). After the research has been stated, then the next step is to complete the null hypothesis, which will contradict the research hypothesis. The third step in testing a hypothesis is to select the sampling distribution and to specify the test statistic. The fourth step is to compute the test statistic following the specified formula to be able to test the statistic. The fifth and final step is to make a decision and to interpret the results. This simply means that we are looking over the results and deciding...
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...more than two means simultaneously. In formulating the hypothesis statement using ANOVA, the team has decided on a null hypothesis that mean net income from the three different financial sectors are equal. After developing the null and alternate hypothesis, Team E preformed the five steps of hypothesis testing using MegaStat and Microsoft Excel (Doane & Seward, 2007). Step 1: State the Hypotheses The hypotheses to be tested are Ho: μt =μf =μe H1: Not all the means are equal (at least one mean is different). Step 2: State the Decision Rule There is c = 3 groups and n = 75 observations, so degrees of freedom for the F test are: Numerator: d.f. 1 = c -1 = 3 -1 =2 (between treatments, factor) Denominator: d.f.2 = n –c = 75 -3 =71 (within treatments, error) Step 3: Select a Level of Significance We will use a = .05 for the test. The 5 percent right-tail critical value from Appendix F is F(3,25) = 3.13 Step 4: Perform the Calculations/ Test Statistics Using MegaStat for the calculations, we obtained the results shown in the Excel Spread sheet. Excels default is a = .05. Step 5: Make the decision Since the test statistic F = 7.60 exceeds the critical value F (.05) = 3.13, we can reject the hypotheses of equal means. The p-value (p = 0.001044) is less than the level of significance (a = .05) which confirms that we should reject the hypothesis of equal treatment means. When using ANOVA. The null hypothesis is that all means are equal. The...
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...terms related to hypothesis testing that you are already familiar with? What is the difference between a null and an alternative hypothesis statement? Why do a null and alternative hypothesis have to be mutually exclusive? (Due Wednesday) Terms that is related to hypothesis testing that I am familiar with is hypothesis, which means a prediction which is usually based on an informal observation, research and it is tested in a study. Theory is another term I know. Theory is what one has or a set of principles that tries to explain one or more facts. I did not know there was something called null hypothesis. According to our textbook, “null hypothesis” is because it “states the situation in which there is no difference ( the difference is null) between the populations” (Aron, Aron, & Coups, 2009). Null hypothesis will show that there is no observed effect for a experiment. A null hypothesis is what one tries to overturn his or her hypothesis test. Taylor (2013) states, “We hope to obtain a small enough p-value that we are justified in rejecting the null hypothesis” (para. 3). A alternative hypothesis is also known as an experimental hypothesis. It shows that there is a observed effect for an experiment. It is what one tries to show in an indirect way by using the hypothesis testing. If the null hypothesis is rejected then one will see that the alternative hypothesis is effective. Now if the finding are not null then one will not accept the alternative of the hypothesis. Reference ...
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