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.... . . . . . . . . . . . . . . . . . . . . 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......

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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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...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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...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,......

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...qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyui opasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfgh jklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvb nmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwerty uiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdf ghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxc vbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwer tyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfg hjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcv bnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwert yuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasd fghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzx cvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwe rtyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdf ghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxc vbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwer tyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopas dfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklz xcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrt yuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasd fghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzx cvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwe rtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopa sdfghjklzxcvbnmqwertyuiopasd......

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.... Use the sales forecaster’s predication to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. Let's assume that the expected sales distribution is normally distributed, with a mean of 20,000, and 95% falling within 10,000 and 20,000. We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by: z = (x - mu)/sigma = 1.96 sigma = (x - mu)/z Sigma = (30,000-20,000) / 1.96 = 5,102 units. So, we have a distribution with a mean of 20,000 and a standard deviation of 5,102. 2. Compute the probability of a stock-out for the order quantities suggested by members of the management team. Using the normal distribution theory, we discover that as the ordered quantity increases the probability of stockout decreases. At 15,000 the probability of stockout will be 0.8365 At 18,000 the probability of stockout will be 0.6517 At 24,000 the probability of stockout will be 0.2177 At 28,000 the probability of stockout will be 0.0582 3. Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales = 10,000 units, most likely case in which sales = 20,000 units and best case in which sales = 30,000 units: Order Quantity: 15,000 were cost price is $16, selling price $24 & after holiday selling price $5 |Unit......

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...Whitners Autoplex Prices Differ from the National Average Team D RES 341 April 18, 2012 Dr. Leroy Paul Whitners Autoplex Prices Differ from the National Average Intro Research Process Consumers purchase new vehicles for many reasons: practicality, functionality, or as a status symbol. Trying to fill that need, Whitners Autoplex is an auto dealer that sells import and domestic automobiles (Lind, Marchal & Wathen, 2008). Buyers, ages 20 to 59, have purchased vehicles at Whitners. Team D, after reviewing the provided data, knows that over the past couple years the car dealer’s average selling price for an automobile was $22,000. Team D’s null hypothesis states that the selling prices in the data set remain unchanged from the established $22,000 average. However, Team D has faith that its alternate hypothesis that the average has changed will prevail. The following will provide the purpose of the research, problem definition, research hypothesis, and a look ahead to the following weeks concerning the study. Using historic and current data, Team D intends to prove the $22,000 average price of a car has changed, and most likely increased due to many factors. If Team D’s alternate hypothesis proves true, then Whitners Autoplex has been charging far more less than surrounding, or even nationwide, auto dealers. Knowing the average cost of a vehicle is important to auto dealers because profit is what allows a business to prosper and......

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...Chapter 9 Hypothesis Tests Solutions: 6. a. H0: μ ≤ 1 Ha: μ > 1 b. Claiming μ > 1 when it is not. This is the error of rejecting the product’s claim when the claim is true. Concluding μ ≤ 1 when it is not. In this case, we miss the fact that the product is not meeting its label specification. H0: μ ≤ 8000 Ha: μ > 8000 b. Research hypothesis to see if the plan increases average sales. The label claim or assumption. c. 7. a. Claiming μ > 8000 when the plan does not increase sales. A mistake could be implementing the plan when it does not help. Concluding μ ≤ 8000 when the plan really would increase sales. This could lead to not implementing a plan that would increase sales. z= x − μ0 = 26.4 − 25 6 / 40 = 1.48 c. 10. a. b. σ/ n Upper tail p-value is the area to the right of the test statistic Using normal table with z = 1.48: p-value = 1.0000 - .9306 = .0694 Using Excel: p-value = 1 - NORMSDIST(1.48) = .0694 c. d. p-value > .01, do not reject H0 Reject H0 if z ≥ 2.33 1.48 < 2.33, do not reject H0 11. a. b. z= x − μ0 σ/ n = 14.15 − 15 3 / 50 = −2.00 Because z < 0, p-value is two times the lower tail area Using normal table with z = -2.00: p-value = 2(.0228) = .0456 9-1 Chapter 9 Using Excel: p-value = 2*NORMSDIST(-2.00) = .0456 c. d. p-value ≤ .05, reject H0 Reject H0 if z ≤ -1.96 or z ≥ 1.96 -2.00 ≤ -1.96, reject H0 15. a. H0: μ ≥ 1056 Ha: μ < 1056 b. z= x − μ0 = 910 − 1056 1600 / 400 = −1.83 σ/ n Lower......

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...Gender Case Processing Summary | | Gender | Cases | | | Valid | Missing | Total | | | N | Percent | N | Percent | N | Percent | Discount | Female | 46 | 100.0% | 0 | 0.0% | 46 | 100.0% | | Male | 54 | 100.0% | 0 | 0.0% | 54 | 100.0% | Descriptives | | Gender | Statistic | Std. Error | Discount | Female | Mean | 1624.57 | 56.376 | | | 95% Confidence Interval for Mean | Lower Bound | 1511.02 | | | | | Upper Bound | 1738.11 | | | | 5% Trimmed Mean | 1619.57 | | | | Median | 1614.50 | | | | Variance | 146197.673 | | | | Std. Deviation | 382.358 | | | | Minimum | 892 | | | | Maximum | 2520 | | | | Range | 1628 | | | | Interquartile Range | 498 | | | | Skewness | .100 | .350 | | | Kurtosis | -.328 | .688 | | Male | Mean | 962.06 | 62.291 | | | 95% Confidence Interval for Mean | Lower Bound | 837.12 | | | | | Upper Bound | 1086.99 | | | | 5% Trimmed Mean | 952.25 | | | | Median | 870.50 | | | | Variance | 209527.261 | | | | Std. Deviation | 457.741 | | | | Minimum | 131 | | | | Maximum | 1990 | | | | Range | 1859 | | | | Interquartile Range | 669 | | | | Skewness | .418 | .325 | | | Kurtosis | -.556 | .639 | Discount Statistics | Discount | N | Valid | 100 | | Missing | 0 | Mean | 1266.81 | Median | 1327.50 | Discount | | Frequency | Percent | Valid Percent | Cumulative Percent | Valid | 131 | 1 | 1.0 | 1.0 |...

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...Statistics Christopher Olson 23 Feb 2015 QNT/351 Statistics in its definitive form is “…the science of learning from data, and measuring, controlling, and communicating uncertainty; and it thereby provides the navigation essential for controlling the course of scientific and societal advances.” (Davidian, M. and Louis, T.A.) Statistics are used for a multitude of reasons in just as many different fields of study and profession. They can range from scientific research in fields of astronomy, engineering, and computer sciences to military strategic applications, and even in situations such as gambling and sports. As once stated by renowned Bell Labs and Princeton scholar John Tukey “The best thing about being a statistician is that you get to play in everyone else’s backyard.” Statistics often play a significantly large role in decision making within the business realm. Statistics are used to analyze trends, and patterns that shape the performance and the future direction of the company. If for instance a company is a production source for an item that is produced and shipped to a particular client, they would more than likely track and forecast production trends. It is noted that one week the facility will have a shortage of primary production employees due to a spike in vacation time being taken. In this situation, management would be able to determine the average production output, and factor in the shortfall that would occur with the employee shortage. From...

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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......

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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......

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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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...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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