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Words 14529

Pages 59

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 the sample design.

Using Samples to Describe Populations:

The following data consists of two samples of house prices, one sample selected from the city of Montreal and the other selected from the West Island:

|Descriptive Statistics - Montreal |

| |…...

...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......

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... * Quantitative is numbers, and qualitative cannot be measured numerically * Descriptive statistics describes sets of data and inferential draws conclusions about the sets of data based on sampling * A population is a set of units interest to a study and a variable is a characteristic or property of the units being studied * A population is a set of existing units and a process produces or generates output over time * A representative sample of n experimental units is a sample selected from the population in such a way that every different sample of size n has an equal chance of selection * Pareto diagram graphs them from highest to lowest * In stem and leaf observations are equal to the number of leafs, count the actual units * Mean, sum/total * Median = middle number when arranged in order * Mode = appears the most times * If data is skewed to the right then the median is less than the mean, symmetric means they are equal, skewed to the left means the mean is less than the median * Range = largest minus smallest * Sample variance, s squared, 1st calculate sample mean, then subtract the mean from each individual number and square that number, add them all up and the divide by n-1 * 1+7+6+6+3+5+3 / 7 = 4.4 * (1 – 4.4)^2 + (7-4.4)^2 + (6-4.4)^2 + (6-4.4)^2 + (3-4.4)^2 + (5-4.4)^2 + (3-4.4)^2 / (7-1) * 11.56 + 6.76 + 2.56 + 2.56 + 1.96 + .36 + 1.96 / 6 = 27.72/6 = 4.62 .32+.78+.63+.31+.38+1.18+.66+.38 / 8 = 4.64/8 =...

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...on the request parameters (and optionally also based on session attributes). 3. The Controller Servlet then by itself or through a controller helper communicates with the middle tier or directly to the database to fetch the required data. 4. The Controller sets the resultant JavaBeans (either same or a new one) in one of the following contexts – request, session or application. 5. The controller then dispatches the request to the next view based on the request URL. 6. The View uses the resultant JavaBeans from Step 4 to display data. Note that there is no presentation logic in the JSP. The sole function of the JSP in Model 2 architecture is to display the data from the JavaBeans set in the request, session or application scopes. [pic] Model 2 Architecture. Advantages of Model 2 Architecture Since there is no presentation logic in JSP, there are no scriptlets. This means lesser nightmares. [Note that although Model 2 is directed towards elimination of scriptlets, it does not architecturally prevent you from adding scriptlets. This has led to widespread misuse of Model 2 architecture.] With MVC you can have as many controller servlets in your web application. In fact you can have one Controller Servlet per module. However there are several advantages of having a single controller servlet for the entire web application. In a typical web application, there are several tasks that you want to do for every incoming request. For instance...

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...Respondents said that regulatory compliance efforts have had a positive effect on their security programs. • By and large, respondents did not believe that the activities of malicious insiders accounted for much of their losses due to cybercrime. 59.1 percent believe that no such losses were due to malicious insiders. Only 39.5 percent could say that none of their losses were due to non-malicious insider actions. • Slightly over half (51.1 percent) of the group said that their organizations do not use cloud computing. Ten percent, however, say their organizations not only use cloud computing, but have deployed cloud-specific security tools. 2 2010 / 2011 CSI Computer Crime and Security Survey about the respondents As always, we note at the outset that this is an informal survey. All surveys of this sort have certain biases in their results. No exception here. The survey was sent to 5412 security practitioners by post and by email, with a total of 351 surveys returned, yielding a 6.4 percent response rate. Assuming that the pool was properly representative of the larger pool of information security professionals and that those returning the form were in turn a random selection of the group, the number of returns would give us 95% confidence in our results with an approximately 5.25% margin of error. In other words, if we could magically find the right answer, then in 19 out of 20 cases it would be within 5.25 percent (either higher or lower) of the number you’ll......

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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 ......

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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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...merchandising and a manufacturing income statement. Indicate how cost of goods manufactured is determined. Explain the difference between a merchandising and a manufacturing balance sheet. Identify trends in managerial accounting. Questions 1, 2, 3 Brief Exercises 1 Do It! 1 Exercises 1 A Problems B Problems *2. 4, 5, 6, 7, 8 11, 12 2, 3 1 *3. 4, 5, 7 2 2, 3, 4, 5, 6 3, 4, 5, 7, 13 8, 12, 13, 14, 15, 17 1A, 2A 1B, 2B *4. 13 6 2 1A, 2A 1B, 2B *5. 9, 14 3A, 4A, 5A 3B, 4B, 5B *6. 15, 16, 17, 18 8, 10, 11 3 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 14, 15, 16, 17 3A, 4A, 5A 3B, 4B, 5B *7. 10, 19, 20, 21 9 3A, 4A 3B, 4B *8. 22, 23, 24 25, 26 4 18 *Note: All asterisked Questions, Exercises, and Problems relate to material contained in the appendix to the chapter. Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only) 1-1 ASSIGNMENT CHARACTERISTICS TABLE Problem Number 1A 2A 3A Description Classify manufacturing costs into different categories and compute the unit cost. Classify manufacturing costs into different categories and compute the unit cost. Indicate the missing amount of different cost items, and prepare a condensed cost of goods manufactured schedule, an income statement, and a partial balance sheet. Prepare a cost of goods manufactured schedule, a partial income statement, and a......

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... d. If the Advertising is $ 800, what are the Sales (Provide Units), Do you have any concerns, explain? e. For what ranges of x-values is the regression equation valid? f. What is extrapolation?. g. If the Advertising is $ 8000, what are the Sales (Provide Units), Do you have any concerns, explain? Question 2 (20 points) – Simple Regression Using Minitab Input the data in Minitab and get the Regression printout for Question 1. Question 3 (45 points) – Simple Regression An economist with Trojan Research wants to develop a simple regression model to predict the food consumption of a household (Y) in thousands of dollars and household Income (X) in tens of thousands of dollars for middle class families. (Note: Food Consumption is in thousands of dollars and Income is in tens of thousands of dollars.) (Xmax = $200,000 and Xmin = $60,000). The average Food consumption is $13,112 Regression Analysis: Food versus Income The regression equation is Food = 12.0 + 0.113 Income Predictor Coef SE Coef T P Constant 12.0238 ______ 28.83 0.000 Income _______ 0.04036 _____ 0.010 S = _______ R-Sq = _____ R-Sq(adj) = 22.1% Analysis of Variance Source DF SS MS F P Regression 1 ______ 4.3235 ______ 0.010 Residual Error ___ ______ 0.5540 Total 24 17.0664 Unusual Observations Obs Income Food Fit SE Fit Residual St Resid 23 20.0 ......

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...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 Policies • Please display your nameplate in every class session until the end of the semester. • You are expected to read through the assigned chapters and familiarize yourself with the content before class. • Please turn off cell phones, pagers, and BlackBerries during class. Out of courtesy to your classmates and your instructor, please come to class on time and do not leave until the class ends, unless you’ve obtained prior permission, and do not engage in private conversations in class. • Anyone caught cheating will be dismissed from the course immediately with a grade of F. Homework / In Class Activities and Participation You are expected to attend every class session and to participate in the discussions. For attending classes without active participation, you can receive no more than 50% of the maximum participation points. In addition, several in-class assignments will be given throughout the semester. Examination • There will be two mid-term examinations in this course and a final exam. The final exam is cumulative but it will be more focused on the material up to the preceding exam. • Both exams will be closed book, notes, laptops, PDAs, etc., except you will be provided with a “cheat sheet”. Calculators are allowed. • Exams are meant to be objective tests of the......

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...use 0.75. Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots below. Calculating Descriptive Statistics Open the class survey results that were entered into the MINITAB worksheet. 2. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here. Mean: 4.600 Standard deviation: 1.429 Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. 3. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not......

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...CHAPTER 9 Step 1: Set up hypotheses testing If you are trying to prove something scientifically, put it in the alternate. If you are challenging a statement, put it in the null. Step 2: The level of significance determines what value of z will be used as the critical value FOR: | TWO TAILED | LOWER TAIL | UPPER TAIL | α=.01 (99% CONF) | Z CRIT = ±2.576 | Z CRIT = -2.33 | Z CRIT = +2.33 | α=.05 (95% CONF) | Z CRIT = ±1.96 | Z CRIT = -1.645 | Z CRIT = +1.645 | α=.10 (90% CONF) | Z CRIT = ±1.645 | Z CRIT = -1.28 | Z CRIT = +1.28 | Step 3: Find your z or t calculated Step 4: Compare Z or T calculated to Z or T critical Reject the null if… TWO TAILED | LOWER TAIL | UPPER TAIL | z calc ≤ -z crit OR z calc ≥ +z crit | z calc ≤ -z crit | z calc ≥ +z crit | Proportions are worked the same way except that they always use z z = | HO TRUE | HO FALSE | ACCEPT HO | Probability = 1-α (confidence)This is correct | Probability = βType II errorConsumer (β) risk | REJECT HO | Probability = αType I errorProducer (α) risk | Probability = 1-β (power of test)This is correct | CHAPTER 10 TWO TAILED | LOWER TAIL | UPPER TAIL | Ho : µ1 = µ2 OR µ1 - µ2 = 0 | Ho : µ1 ≥ µ2 OR µ1 - µ2 ≥ 0 | Ho : µ1 ≤ µ2 OR µ1 - µ2 ≤ 0 | Ha : µ1 ≠ µ2 OR µ1 - µ2 ≠ 0 | Ha : µ1 < µ2 OR µ1 - µ2 < 0 | Ha : µ1 > µ2 OR µ1 - µ2 > 0 | The point estimate for sample differences......

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...Assignment 08 MA260 Statistical Analysis I Directions: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the "Assignment Format" page located on the Course Home page for specific format requirements. NOTE: Show your work in the problems. 1. A recent article in the Myrtle Beach Sun Times reported that the mean labor cost to repair a color television is $90 with a standard deviation of $22. Monte’s TV Sales and Service completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. Compute z values for each and comment on your findings. 2. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds? 3. The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels? 4. Research on new juvenile delinquents revealed that 38% of them......

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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......

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...individual regression coefficients (using the individual p-values); the confidence intervals of the individual regression coefficients; and the 95% prediction and confidence intervals, for particular values of the independent variables (which you select). 8) Add a brief, well written introduction and conclusion. 9) Be sure that all the writing is yours (check my Announcement from Week 1: “How to Avoid Too Much Copy and Paste”). 10) If it would be helpful to you, I will provide you with feedback on your statistical analysis prior to your submission of the Final Project. I will only look at the statistical analysis, to give you feedback as to whether you are on the right track. Send it to me as an email, with an attachment, and your brief notes and questions on the analysis. If you don’t hear from me in 24 hours, it means it has gotten lost, so send it again, or call me. Due to limitations on my time, I will not be able to review and correct the quality of your writing in your draft (though this will be an important part of your final grade on the Course Project). You need to carefully review your own writing, including asking others to read it and provide you with honest feedback, as you would prior to submitting a report to your manager. The keys to earning top points on your writing are: a) that it be well written, and b) that it be written in plain English, as to a manager who has very little to no understanding or knowledge of statistics, though you should......

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...Stats/Modelling Notes Introduction & Summary Computer system users, administrators, and designers usually have a goal of highest performance at lowest cost. Modeling and simulation of system design trade off is good preparation for design and engineering decisions in real world jobs. In this Web site we study computer systems modeling and simulation. We need a proper knowledge of both the techniques of simulation modeling and the simulated systems themselves. The scenario described above is but one situation where computer simulation can be effectively used. In addition to its use as a tool to better understand and optimize performance and/or reliability of systems, simulation is also extensively used to verify the correctness of designs. Most if not all digital integrated circuits manufactured today are first extensively simulated before they are manufactured to identify and correct design errors. Simulation early in the design cycle is important because the cost to repair mistakes increases dramatically the later in the product life cycle that the error is detected. Another important application of simulation is in developing "virtual environments" , e.g., for training. Analogous to the holodeck in the popular science-fiction television program Star Trek, simulations generate dynamic environments with which users can interact "as if they were really there." Such simulations are used extensively today to train military personnel for battlefield situations, at a......

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