.... . . . . . . . . . . . . . . . . . . . . 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 statistic, the less compatible the data is with the null hypothesis. Most test statistics...
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...STAT 346/446 - A computer is needed on which the R software environment can be installed (recent Mac, Windows, or Linux computers are sufficient).We will use the R for illustrating concepts. And students will need to use R to complete some of their projects. It can be downloaded at http://cran.r-project.org. Please come and see me when questions arise. Attendance is mandatory. Topics covered in STAT 346/446, EPBI 482 Chapter 5 – Properties of a Random Sample Order Statistics Distributions of some sample statistics Definitions of chi-square, t and F distributions Large sample methods Convergence in probability Convergence in law Continuity Theorem for mgfs Major Theorems WLLN CLT Continuity Theorem Corollaries Delta Method Chapter 7 – Point Estimation Method of Moments Maximum Likelihood Estimation Transformation Property of MLE Comparing statistical procedures Risk function Inadmissibility and admissibility Mean squared error Properties of Estimators Unbiasedness Consistency Mean-squared error consistency Sufficiency (CH 6) Definition Factorization Theorem Minimal SS Finding a SS in exponential families Search for the MVUE Rao-Blackwell Theorem Completeness Lehmann-Scheffe Location and scale invariance Location and scale parameters Cramer-Rao lower bound Chapter 9 - Interval Estimation Pivotal Method for finding a confidence interval Method for finding the “best” confidence interval Large sample confidence intervals ...
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...STAT 302 – Statistical Methods Lecture 8 Dr. Avishek Chakraborty Visiting Assistant Professor Department of Statistics Texas A&M University Using sample data to draw a conclusion about a population • Statistical inference provides methods for drawing conclusions about a population from sample data. • Two key methods of statistical inference: o o Confidence intervals Hypothesis tests (a.k.a., tests of significance) Hypothesis Testing: Evaluating the effectiveness of new machinery at the Bloggs Chemical Plant • Before the installation of new machinery, long historical records revealed that the daily yield of fertilizer produced by the Bloggs Chemical Plant had a mean μ = 880 tons and a standard deviation σ = 21 tons. Some new machinery is being evaluated with the aim of increasing the daily mean yield without changing the population standard deviation σ. Hypothesis Testing: Evaluating the effectiveness of new machinery at the Bloggs Chemical Plant Null hypotheses • The claim tested by a statistical test is called the null hypothesis. The test is designed to assess the strength of the evidence against the null hypothesis. Usually the null hypothesis is a statement of “no effect” or “no difference”, that is, a statement of the status quo. Alternative hypotheses • The claim about the population that we are trying to find evidence for is the alternative hypothesis. The alternative hypothesis is one-sided if it states that a parameter is larger than or...
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...SAMPLE MULTI-YEAR LEASE AGREEMENT This Lease Agreement is entered into on this ___ day of _____________, 2009, by and between ________________ as lessor (“Lessor”), and____________________, as lessee (“Lessee”), for the Lease of certain land bounded by ____________in _______________, for the purpose of establishing and developing an agricultural enterprise. I. Prologue and Statement of Purpose Whereas both parties share a mutual interest in the long-term health and productivity of the agricultural lands and related features described below; and whereas the Lessor wishes to offer a secure and affordable farming opportunity to the Lessee; and whereas the Lessor wishes the property to be maintained according to high standards of stewardship, the parties agree as follows: II. Description of Leased Premises a) The Premises shall consist of cropland and other land, roads and structures as more particularly described in Attachment A. b) If applicable: So that the Lessee can reside in close proximity to the land and provide for its care and supervision, Lessor and Lessee shall also be parties to a separate residential lease agreement for a term beginning on _________ and ending on ____________ for the farmhouse property located at ________________ (the “Residential Lease”). If the parties agree to an extension of the term of this Lease, either via an amendment to this Lease or the execution of a new lease between the parties, Lessor shall also offer Lessee an extension of the Residential...
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...2010 / 2011 CSI Computer Crime and Security Survey 15th annual 2010/2011 Computer CrIme and SeCurIty Survey www.GoCSI.com 1 2010 / 2011 CSI Computer Crime and Security Survey by Robert Richardson, CSI Director 2010 / 2011 CSI Computer Crime and Security Survey With this document, the CSI Survey achieves its fifteen-year mark. Both the aims and format of the survey continue to evolve. As you’ll see in the findings that follow, many of the results reported by our respondents easily could have been predicted based on looking at results from the past several years. There has always been an almost surprising stability to answers about tools and methodology in this survey and this year is not an exception. What is different, broadly speaking, is that there is considerably more context within which these results may be interpreted. There are a number of very good reports of various kinds now available on the Web. All of them that we’re aware of, with the exception of this one, are either provided by vendors or are offered by analyst firms. That’s not to say that there’s anything wrong with these sources. A tremendous amount of useful information is offered in these various reports. But independent research seems fundamental and we believe the survey provides this. Beginning last year, there were three important changes to this survey. The first was that a “Comprehensive” edition was offered, one of its key objectives being to attempt to take other report findings...
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...Gallup Poll. June 1-4, 2013. N=1,529 adults nationwide. Margin of error 3. "How closely have you followed the news that the Internal Revenue Service, or IRS, gave greater scrutiny to conservative political groups applying for tax exempt status than it did to liberal political groups: very closely, somewhat closely, not too closely, or not at all?" Very closely Somewhat closely Not too closely Not at all Unsure % % % % % 6/1-4/13 20 34 24 21 1 "How serious do you consider the IRS giving greater scrutiny to conservative political groups applying for tax-exempt status: very serious, somewhat serious, not too serious, or not serious at all?" Very serious Somewhat serious Not too serious Not serious at all Unsure % % % % % 6/1-4/13 49 28 12 7 4 "Do you think high-ranking Obama administration officials were aware of IRS targeting of conservative groups, or do you think knowledge of the practice was mainly limited to IRS employees in the Cincinnati office where applications for tax-exempt status are processed?" N=755 margin of error 4 High-ranking officials were aware Mainly Cincinnati employees Unsure % % % 6/1-4/13 50 36 14 "Do you think high-ranking IRS officials in Washington were aware of IRS targeting of conservative groups, or do you think knowledge of the practice was mainly limited to IRS employees in the Cincinnati office where applications...
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...1. This question pertains to the following SPSS output from a One Sample t-test used to obtain a confidence interval for a mean. |One-Sample Statistics | | |N |Mean |Std. Deviation |Std. Error Mean | |Probability of buying a standard |1000 |30.12 |21.205 |.671 | |size hybrid auto within 3 years | | | | | |One-Sample Test | | |Test Value = 0 | | | | |N |Mean |Std. Deviation |Std. Error Mean | |Probability of buying a standard |1000 |34.64 |22.090 |.699 | |size electric auto within 3 years | | | | | |One-Sample Test ...
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...Forcing early retirements Forcing early retirement is a huge problem, there are rumours that there is a case of forcing early retirements at Loxley. Forcing early retirement is the involuntary ending of one's career because of a layoff, health problems or disability. Age discrimination means employers fail to hire or promote a worker or avoid training a staff member based on his age. Forcing an employee into early retirement based exclusively on age is also discriminatory. Employer discrimination also involves firing an employee or forcing the staff member to quit before earning company retirement benefits. One of the reasons why older workers would be forced into early retirements is due to the fact that younger workers earn less pay compared with senior workers and managers. Eliminating a division of senior staff saves money and also eliminates imminent company retirement benefits by letting the older workers go before the official retirement age. Using the bottom 10 employees as a sample of the entire 144 employees, we find that the correlation between the number of years an employee is at the company is lowly correlated with their performance score. The correlation coefficient is 0.2071 The top 10 employees’ correlation coefficient is 0.2964 This tells us that the number of years that an employee has been with the company does not affect the employees’ score by much. This leads to reason that the rumors about the company forcing early retirements have no substance...
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...Chapter one, What is Strategy? • What is our present situa4on? – Business environment and industry condi4ons – Firm’s financial and compe44ve capabili4es • Where do we want to go from here? – Crea4ng a vision for the firm’s future direc4on • How are we going to get there? – CraBing an ac#on plan that will get us there The Strategy-‐Making, Strategy-‐Execu4ng Process 1 WHAT IS STRATEGY ABOUT? • Strategy is all about – How to outcompete rivals. – How to respond to economic and market condi4ons and growth opportuni4es. – How to manage func4onal pieces of the business. – How to improve the firm’s financial and market performance. WHY DO STRATEGY ? • A firm does strategy: – To improve its financial performance. – To strengthen its compe44ve posi4on. – To gain a sustainable compe44ve. advantage over its market rivals. • A crea4ve, dis4nc4ve strategy: – Can yield above-‐average...
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...NORTHEASTERN UNIVERSITY - GRADUATE SCHOOL OF BUSINESS ADMINISTRATION MGSC 6200: DATA ANALYSIS Spring, 2015 Instructor Information Name: Dr. Nizar Zaarour E-mail address: n.zaarour@neu.edu Office: 214 Hayden Hall Office hours: Monday and Wednesday: 12 – 2 PM and by appointment. Course Overview The objectives of this course are: (1) To provide you with an understanding of statistical methods and techniques and their usefulness in the decision-making process, (2) To expose you to the methods of descriptive and inferential statistics and how can be used to solve business problems, (3) To improve upon your data analysis and computer skills, (4) To help you develop the skills to recognize the appropriate statistical tool to analyze business problems, and (5) To provide you with the necessary tools for critical evaluation, correct interpretation, and presentation of the results of statistical analyses. Textbook and Software 1) Business Statistics: For Contemporary Decision Making, 7th Edition, by Ken Black, (Wiley). 2) Microsoft Excel. Course Organization The course web page is located in the Blackboard system at http://blackboard.neu.edu. Course materials and announcements will be posted on the course site. A Blackboard tutorial is available at http://www.discoveringblackboard.neu.edu. The textbook is quite easy to read and covers a lot of ground. However, some of the topics are not covered in depth. Class discussions, handouts, and my lecture notes will fill these gaps. Course...
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...Clara Arias Business Statistics February 1, 2016 Nielsen Reflection While exploring Nielsen I realized the importance of knowing what we as consumers watch and buy. I personally don’t really watch TV at all; probably just a couple of shows but TV is not essential in my life. When I clicked on “Cable Network TV” I first saw these two programs called “Gold Rush” and “The Oreilly Factor” then the only thing I did was looked up these programs and read something about them since I didn’t really know about their existence. It’s probably unbelievable to you hearing this from me because nowadays almost everybody watches TV and everyone is aware of what is in the news. While looking up about “Gold Rush” I noticed it wasn’t a new series, it had actually been released since 2010 and now it is composed of 6 episodes. I think I should start watching TV since I felt I have been missing tons of stuff. In addition to this program I think it is essential to say that the network involved is “Disc”. I also went to look for most popular music and of course the first thing I saw was Justin Bieber with his song “Be yourself”, I usually listen to this song almost everyday because it is actually popular, but after knowing it is in the first place of ranking list I couldn’t help the craving of knowing how many reproductions it has on Youtube. Well it has about 247,768,905 reproductions in just 3 months, isn’t that crazy? I guess people are not surprised anymore about Justin’s fame. Another...
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...CASES DISPOSED, APPEALED, AND REVERSED IN HAMILTON COUNTY COURTS Common Pleas Court Judge Fred Cartolano Thomas Crush Patrick Dinkelacker Timothy Hogan Robert Kraft William Mathews William Morrissey Norbert Nadel Arthur Ney, Jr. Richard Niehaus Thomas Nurre John O� Connor Robert Ruehlman J. Howard Sundermann Ann Marie Tracey Ralph Winkler Total Total Cases Disposed 3,037 3,372 1,258 1,954 3,138 2,264 3,032 2,959 3,219 3,353 3,000 2,969 3,205 955 3,141 3,089 43,945 Appealed Cases 137 119 44 60 127 91 121 131 125 137 121 129 145 60 127 88 1,762 Reversed Cases 12 10 8 7 7 18 22 20 14 16 6 12 18 10 13 6 199 Common Pleas Court disposed 43, 945 total cases. The total number of cases appealed was 1,762, and the total number of cases reversed was 199. In all cases disposed in the Common Pleas Court, the probability of cases could be appealed and reversed is? Total reversed cases/ Total appealed cases= 199/1762= 0.11294 or 11.2% Domestic Relations court disposed a total of 30,499 cases. The total number of cases appealed was 106, and the total number of cases reversed was 17. In all cases disposed in the Domestic Relations Court, the probability of cases could be appealed and reversed is: Total reversed cases/ Total appealed cases=17/106= 0.16037 or 16% Municipal Court disposed of a total of 108,464. The total number of cases they appealed was 500, and the total number of cases reversed was 104. In all cases disposed in the Municipal Court, the probability of cases could be...
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...BUAD 310 – Spring 2011 - Dr. Arif Ansari Topics Covered –Simple Regression Homework # 4 - 100 points (Due date 4/4/2011- Monday) For Home Work 4, Turn in Part 1 (15 points), Question 1(20 points), Question 2 (20 points), Question 3 45 points). Part 1 MULTIPLE CHOICE [3 point each] 1. In Least squares regression, the regression line is obtained by minimizing, a) The total variation in the dependent variable. b) The sum of squares for error (SSE). c) The sum of squares for regression (SSR) d) The sum of squares for total (SST). e) None of the above 2. In a simple regression analysis involving 25 data points, the standard error of estimate is calculated as S( = 2.0 and the Fts = 10, then the information from regression line (SSR) should be, a) 60 b) 50 c) 40 d) 30 e) None of the above 3. In a statistics course, a linear regression equation was computed to predict the final exam score from the first quiz score. The equation obtained was Y = 10 + 0.9 X, where Y is the final exam score and X is the first quiz score. A prediction interval for Al Bundy who scored 95 on the first quiz and on the final exam scored 98 was computed. Also a confidence interval for mean score of 95 on the first quiz was computed. From this we can conclude: a) Al Bundy’s prediction interval in wider than the confidence interval. b) Al Bundy’s prediction interval in shorter than the confidence interval...
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...Factors that Affect Credit Score? FICO makes the formulas and programs for all credit reporting agencies. The names of formulas and actual procedures are different from agency to agency, the basic factors affecting credit score are however the same and the basic formula and its constituents remain the same. The three different models for credit scoring by FICO include, BEACON score used by Equifax, Experian/Fair Isaac Risk Model used by Experian and EMPIRICA used by TransUnion. The companies do not disclose the exact formulas but as per FICO resources, the following are the things that make up a credit score and also tend to affect the score. * Payment History (35%): The payment history basically consists of all your past accounts and the regularity with which payments have been made. A bad and irregular payment history causes the score to drop down. * Amounts Owed (30%): The total amount of debts owed to other lenders is also an important consideration in the score calculation. The standard equation is, more the amounts owed, less is the credit score. Hence keep the credit history and current liabilities to the bare minimum. * Length of Credit History (15%): The length of the credit history is also considered. Rule of the thumb is that longer the history, lesser is the score. Thus avoid unnecessary borrowings and keep them to the bare minimum. * New Credit (10%): New credit consists of the newly borrowed loans or newly taken up credit cards. Keeping it small always helps, as...
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...DESC 471 ONE OPEN NOTE TEST #1 120 MINUTES FALL 2011 NAME _____________________ TEST SCORE _________ CENTER: ENCINO HMWK% ________ SEM GRADE __________ w/RETEST=100 ________ USE PENCIL!! USE PENCIL!! USE PENCIL!! USE PENCIL!! USE PENCIL!! Show work for partial credit 1. (20 points) Answer the following questions: Circle the correct T/F answer. Don’t leave any questions uncircled! No penalty for guessing! (1 point each) a) T F If kurtosis is > 1, then the data must be exponential. b) T F The Interquartile Range (IQR) is Q3-Q1. c) T F There is no built-in Excel function for the range of a data set. d) T F Outliers have to be outside both the 6-sigma and Tukey limits. e) T F Pivot Tables are limited to a maximum of 10 rows and 10 columns. f) T F Frequency graphs can determine the mode, Box & Whiskers does not. g) T F The birth data from the Anaheim Ducks and Los Angeles Kings proved Outliers was correct. h) T F For the Hypergeometric distribution the value of p changes each time an object is selected. i) T F Heights of adult males is a good example of the Poisson distribution. j) T F When children give their age, it’s continuous; for adults it’s integer. k) T F If a LUMAT template cell is colored, you can enter data or labels. l) T F The...
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