...the geometric mean, and weighted means, among other things. Chi-square Statistic. The chi-square statistic is used to measure the agreement between categorical data and a multinomial model that predicts the relative frequency of outcomes in each possible category. Suppose there are n independent trials, each of which can result in one of k possible outcomes. Suppose that in each trial, the probability that outcome i occurs is pi, for i = 1, 2, … , k, and that these probabilities are the same in every trial. The expected number of times outcome 1 occurs in the n trials is n×p1; more generally, the expected number of times outcome i occurs is expectedi = n×pi. If the model be correct, we would expect the n trials to result in outcome i about n×pi times, give or take a bit. Let observedi denote the number of times an outcome of type i occurs in the n trials, fori = 1, 2, … , k. The chi-squared statistic summarizes the discrepancies between the expected number of times each outcome occurs (assuming that the model is true) and the observed number of times each outcome occurs, by summing the squares of the discrepancies, normalized by the expected numbers, over all the categories: chi-squared = (observed1 − expected1)2/expected1 + (observed2 − expected2)2/expected2 + … + (observedk − expectedk)2/expectedk. As the sample size n increases, if the model is correct, the sampling distribution of the chi-squared statistic is approximated increasingly well by the chi-squared curve with (#categories...
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...Notes for Statistics 3011 University of Minnesota Fall 2012 Section 010 Instructor: Shanshan Ding Notes accompany the Third Edition of Statistics: The Art and Science of Learning From Data by Alan Agresti and Christine Franklin 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...
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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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...Unit 4 – Hypothesis Testing & Variance Abstract There are two tests that are preformed following a two-tailed hypothesis test, using a .05 significance level. The first test is intrinsic by gender and the second is extrinsic variable by position type. This section will be taking a closer look at intrinsic satisfaction by gender and extrinsic satisfaction by position. Separate hypothesis test will be performed on both variances with the outcomes. Hypothesis Test #1 Looking at Intrinsic Satisfaction by Gender H0:Males= μ Females H1:Males= μ Females ∝ = .05 Significance level: 0.05 T statistic: 2.05 Critical T values: -1.98 and 1.98 P value: 0.04 Since the test statistics of 2.05 is greater than critical value of 1.98 we reject to reject the Ho. The decision made for the intrinsic job satisfaction survey, which intrinsic is when one does it for one’s satisfaction. The data says that it does not support the intrinsic Ho. The p value is less than the alpha. Managers for this business could use this information specifically to help drive the motivation of their employees. This information could show value in the growth of the company with having employees that enjoy their job and complete for their own satisfaction not for reasons such as outside rewards could say a lot about working for this company. If employees first enjoy their job this could mean greatness for the company, employees will strive to better the company and their self-worth...
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...highly essential in statistics. In order to properly conduct research, we must accurately complete the steps in 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...
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...the last four weeks is as follows: The Steps in Testing a Research Hypothesis Hypothesis testing begins with a statement and assumption that determines the population of the mean, (Lind, 2011, p.288.). The five steps listed in Lind are as follows: 1. State null and alternate hypothesis 2. Select a level of significance 3. Identify the test statistic 4. Formulate a decision rule 5. Take a sample and arrive at decision However in McClave, 2011, pages 324 and 325 the steps for testing of a hypothesis are listed as “Elements of a Test of Hypothesis” and instead of five steps they list seven. The seven steps from McClave are listed as follows: 1. Null hypothesis: A theory about the specific values of one or more population parameters. The theory generally represents the status quo, which we adopt until it is proven false. The theory is always stated as Ho: parameter = value. 2. Alternative (research) hypothesis (Ha): A theory that contradicts the null hypothesis. The theory generally represents that which we will adopt when sufficient evidence exists to establish its truth. 3. Test statistic: A sample statistic used to decide whether to reject the null hypothesis. 4. Rejection region: The numerical values of the test statistic for which the null hypothesis will be rejected. The rejection region is chosen so that the probability α is that it will contain the test statistic when the null hypothesis is true, thereby leading to Type I error. The value of α is usually...
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...|Individual Fundamentals of |Write a 700- to 1,050-word paper describing the scientific method and the fundamentals of |Mon, 11/18/2013 |10 | |Research Paper |research. Address each of the following in your paper: |11:59 PM MST | | | | | | | | |Define the scientific method. How does it relate to human services research? | | | | | | | | | |What are the steps in the process of scientific inquiry? Why must each of these steps be | | | | |included to support the scientific method? Provide a human services research example of the | | | | |scientific method and identify each step within your example. | | | | | | | | | |Define quantitative research...
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...Running head: BOTTLING COMPANY CASE STUDY 1 Bottling Company Case Study BOTTLING COMPANY CASE STUDY 2 Abstract In this assignment, I am a manager at a major bottling company and the customers have begun to make complaints that the bottles of the brand of soda produced at the company I work for have less than the advertised 16 ounces of soda. My boss wants me to solve the problem and has asked me to investigate into the situation. I have the employees on the floor pull 30 bottles off the line at random from every shift which I assume is from three shifts and I have asked the employees involved to measure the amount of soda there is in each of the 30 bottles. The Mean, Median and Standard Deviation The mean or average of a data set is simply the average of all the numbers in the set. To find the average mean add up all the numbers in the data set and divide by how many numbers in the set. In this situation, there are 30 bottles with the weight of 14.5, 14.6, 14.7,14.8,14.9,15.3,14.9, 15.3, 14.9,15.5,14.8,15.2,15,15.1,15,14.4,15.8,14,16,16,15.8,14.5,14.1,14.2,14,14.9,14.7,14.5, 14.6,14.8, and 14.6. The total is 446.1 and divided by 30 and the mean is 14.87. The median is calculated by arranging the data in order and selecting the middle point and in this data set the median is an even number so we have to add the...
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...4/7/2014 Basic Statistics: An Overview Basic Statistics: Review Descriptive Statistics Scatter graph Measures of central tendency Mean Median, quartile, deciles, percentile Mode Weighted mean GM HM Measures of dispersion Range, IQR Semi IQR Mean deviation Standard deviation Variance Coeff of variation Inferential Statistics Populations Sampling Estimation of Parameters Point Estimation Interval Estimation Unbiased Minimum Variance Consistency Efficiency Properties of Point Estimators Statistical Inference: Hypothesis Testing T test F test Chi square test Measures of shape of the curve Moments Skewness kurtosis Probability distributions Normal Distribution T-student Distribution Chi-Square Distribution F Distribution Index Number Etc. Correlational Statistics Covariance Correlations regressions 1 4/7/2014 Some Terminology Variables are things that we measure, control, or manipulate .They may be classified as: 1. Quantitative i.e. numerical Continuous: takes fractional values ex. height in cm Discrete : takes no fractional values ex. GDP Random Variable: If the value of a variable cannot be predicted in advance Non random : If the value of a variable cannot be predicted in advance Some Terminology 2. Qualitative i.e. non numerical 1. Nominal: Items are usually categorical and may have numbers...
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...2015 Terrance Feravich Introduction As team C finishes week four of statistics 351, we have reviewed various aspects of testing a research hypothesis. Team C has also reviewed how to compare means of two or more groups and calculate the correlation between two variables. Team C has discussed some concepts that the team has struggled with and fully understood. Team C has also come to understand how this concept can be beneficial to their careers and how they may apply to improve productivity. The steps in testing a research hypothesis "Hypothesis testing starts with a statement, or assumption, about a population parameter - such as the population mean." (Lind, 2011). The purpose of testing the hypothesis is to determine whether to reject or not reject the hypothesis. The hypothesis itself is an assumption. That is; you are determining what the outcome will be given your current knowledge and understanding prior to testing it and obtaining results from those tests. Initially, one will state the null and alternative hypothesis. The null hypothesis, in this case, represents a statement about the value of a population parameter developed for the purpose of testing numerical evidence. The alternative hypothesis is then accepted if the sample data has enough evidence to show that the null hypothesis is false. The next step is to state the level of significance or the probability of rejecting the null hypothesis when it is true. It is important to determine the level of significance...
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...Descriptive Statistics Descriptive statistics involves organizing, summarizing and illustrating statistical data. The objective is to show important characteristics of the data without drawing any conclusions. Inferential statistics involves using a representative subset of data (a sample) in order to draw conclusions about unknown characteristics of an entire set of data (a population). Population: The entire set of elements of interest (i.e. all humans, all working-age people in Canada, all IT companies). A population parameter is a characteristic used to describe a population. For example, Population mean ( Population standard deviation ( Population median ( The values of the population parameters would be preferable for use in decision-making but seldom will these values be known since collecting all the population elements (a census) is usually too expensive and/or time consuming. Sample: A representative subset of the entire set of elements of interest that is used to gain insight about the population. A sample statistic is a characteristic used to describe a sample. For example, Sample mean [pic] Sample standard deviation s Sample median Md It is cheaper, less time-consuming and more practical to use sample statistics as estimates for population parameters in making business decisions. How well the sample represents the population depends on...
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...artists. The team realizes that the variables of male versus female country artists may give the record label an overall view for that genre of music videos being viewed. Research Question Is the difference in the number of YouTube views (DV) based on the gender of the artists (IV)? Hypotheses H0: The difference in YouTube views (DV) is not based on the gender of the artist (IV). H1: The difference in YouTube views (DV) is based on the gender of the artist (IV). Part 2: Literature Review Literature Review This article formulates the understanding that when comparing two populations of vast amounts data its statistical study can be supported by the central limit theorem (Tsung-Shan, 2003). Robust statistics is a convenient way of determining a central tendency and its dispersion; it also...
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...little to no experience on the business end of owning a car dealership. It has been reported that Tom’s asking prices for his vehicles are not aligned with the average market price. Ultimately, Tom does not base his prices on the used car market price; instead he bases it on assumptions. For example, Tom thinks, red cars give the impression of being “sportier and can sell at a premium,” he also believes older models normally sell for less. After much dismay and inaccurate rates in sells, Tom tries to systematically price his Mustangs, but due to the multitude of variables, Tom found this task challenging. (Bowerman, 2003, p. 3) This report will provide information obtained through hypothesis confidence intervals and hypothesis testing, multiple and simple regression models, descriptive statistics, and historical background information pertaining to Tom’s Ford Mustangs. This report will pay close attention to the possible relationship between the dependent...
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...Population parameters • Standard errors • Systematic estimates • Sample statistics Find the Latest Final Exam answers here QNT 565 Final Exam (Latest) 3. A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is • 36.82 • 22.86 • 5.16 • 6.07 4. If the hypothesis presented is tested using a .05 alpha level and the resulting p value is .01, which of the following interpretations of the results is most appropriate? • As income increases, food expenditures increase. • There is a relationship between income and food expenditures. • As income decreases, the percentage of income spent on food increases. • There is no relationship between income and food expenditures. 5. Paired comparison scales result in _____ data. • ratio • interval • ordinal • nominal To download the Complete Assignment of QNT/565 Class check QNT 565 Entire Course 6. Five homes were recently sold in Oxnard Acres. Four of the homes sold for $400,000 while the fifth home sold for $2.5 million. Which measure of central tendency best represents a typical home price in Oxnard Acres? • The mean or mode. • The midrange or mean. • The median or mode. • The mean or median. 7. An increase in hours of television viewing leads to increases in the sales of snack foods. This is an example of a • causal hypothesis • correlational hypothesis • research question • descriptive hypothesis Want to download the Complete Final Exam Assignment..?? Click...
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...and statistics are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is of mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory. Probability (or likelihood) is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen. These concepts have been given an axiomatic mathematical derivation in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems. Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. The word statistics, when...
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