...Teaching Statistics and Probability is great for promoting problem solving and critical thinking, enhancing communication, developing number sense, and applying computation. As it applies to every day situations and appeals to our sense of fairness, it is very close in nature to inquiry based learning. Children encounter ideas of statistics and probability outside of school every day. The data students see are often represented graphically, statistically, or probabilistically. Weather reports are just one example of probability data we hear on the news. Begin teaching probability by formulating questions. “How many children in this class prefer to eat apples?” Children are familiar with line plots, which they learned earlier, review and build on that knowledge. Next step in teaching probability is to teach to collect data: observations, survey and questionnaires, experiments, interviews, simulations, poles, examining records, and searching info sources. It is important to teach kids to use appropriate methods of collecting data. Next step is to analyze data, represent it graphically. Representing data is done in a concrete way first (laying objects on the graph), and moving towards pictorial representation (drawing a chart with pictures of items being compared), and then symbolic (line plot, pie chart). Help students understand graphic representations by asking questions about the chart. Different ways to represent graphically: line plots, stem and leaf plots, box plots, picture...
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...Economics 30330: Statistics for Economics Problem Set 8 - Suggested Solutions University of Notre Dame Instructor: Julio Gar´ ın Spring 2012 Hypothesis Testing (80 Points) 1. Consider the following hypothesis test: H0 : µ ≥ 20 HA : µ < 20 A sample of 40 provided a sample mean of 19.4. The population standard deviation is 2. (a) Create a 95% confidence interval for the mean. We know σ, therefore we should use the z − table. This is a one-tailed (lower tail) test, so the 95% confidence interval will be given then by σ x − z.05 √ , ∞ ¯ n 2 19.4 − 1.65 √ , ∞ 40 The 95% confidence interval is µ ∈ [18.878, ∞). (b) What is the p-value? The p-value is the area in the lower tail. First, we calculate the z-value: z= 19.4 − 20 √ = −1.9 2/ 40 Using the normal table with z = -1.9, p-value =.0287. (c) At α = 0.01, what is your conclusion? p-value > .01, so we fail reject H0 at the 99% level. (d) What is the rejection rule using the critical value? What is your conclusion? c Reject H0 at the 99% level if z ≤ zα =-2.33. In this example, -1.9 > -2.33, so we fail to reject H0 at the 99% level. 2. Consider the following hypothesis test: H0 : µ = 15 HA : µ = 15 A sample of 50 provided a sample mean of 14.5. The population standard deviation is 3. 1 (a) Create a 95% confidence interval for the mean. We know σ, therefore we should use the z − table. This is a two-tailed test, so the 95% confidence interval will be given then by σ σ x − z.025 √ , x +...
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...Problem Books in Mathematics Edited by P. Winkler Problem Books in Mathematics Series Editors: Peter Winkler Pell’s Equation by Edward J. Barbeau Polynomials by Edward J. Barbeau Problems in Geometry by Marcel Berger, Pierre Pansu, Jean-Pic Berry, and Xavier Saint-Raymond Problem Book for First Year Calculus by George W. Bluman Exercises in Probability by T. Cacoullos Probability Through Problems by Marek Capi´ski and Tomasz Zastawniak n An Introduction to Hilbert Space and Quantum Logic by David W. Cohen Unsolved Problems in Geometry by Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy Berkeley Problems in Mathematics (Third Edition) by Paulo Ney de Souza and Jorge-Nuno Silva The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004 by Duˇan Djuki´, Vladimir Z. Jankovi´, Ivan Mati´, and Nikola Petrovi´ s c c c c Problem-Solving Strategies by Arthur Engel Problems in Analysis by Bernard R. Gelbaum Problems in Real and Complex Analysis by Bernard R. Gelbaum (continued after subject index) Wolfgang Schwarz 40 Puzzles and Problems in Probability and Mathematical Statistics Wolfgang Schwarz Universit¨ t Potsdam a Humanwissenschaftliche Fakult¨ t a Karl-Liebknecht Strasse 24/25 D-14476 Potsdam-Golm Germany wschwarz@uni-potsdam.de Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA Peter.winkler@dartmouth.edu ISBN-13: 978-0-387-73511-5 e-ISBN-13: 978-0-387-73512-2 ...
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...Learning Team Assignment: Learning Team Assignment MTH 233 Week 4 Individual Assignment: Individual Assignment MTH 233 Week 5 Individual Assignment: Individual Assignment MTH 233 Week 5 Learning Team Assignment: Hypothesis Testing and Regression Analysis Paper only MTH 233 Learning Team Assignment: Hypothesis Testing and Regression Analysis Presentation ----------------------------------------------- MTH 233 Learning Team Assignment Hypothesis Testing and Regression Analysis Presentation For more classes visit www.snaptutorial.com Resources: University Library and the Internet Select a research issue, problem, or opportunity facing a Learning Team member’s organization to examine using hypothesis testing and a regression analysis on the collected data. Write a 1,050- to 1,750-word paper describing a new hypothesis test using a different statistic (e.g., large sample size, small sample size, means and/or proportions, one- and two-tailed tests) to perform on that data. Formulate a new hypothesis statement and perform the five-step hypothesis test on the data. Describe the results of the tests. Interpret the results of the regression analysis, state the limitations of the analysis, and describe the significance of the results to the organization. Be sure to attach the results of the regression analysis created in Microsoft® Excel to your paper. Present the results to the class in a 10-minute PowerPoint® presentation ----------------------------------------------- ...
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...snaptutorial.com PSYCH 625 Week 1 Individual Assignment Basic Concepts in Statistics Worksheet PSYCH 625 Week 1 Individual Assignment Reliability and Validity Matrix PSYCH 625 Week 1 Individual Assignment Time to Practice – Week One PSYCH 625 Week 2 Individual Assignment Time to Practice – Week Two PSYCH 625 Week 2 Learning Team Assignment Statistics Project Import Data Into IBM ® SPSS ® Software PSYCH 625 Week 3 Individual Assignment Time to Practice – Week Three PSYCH 625 Week 3 Learning Team Assignment Hypothesis Testing Problem Worksheet PSYCH 625 Week 3 Learning Team Assignment Statistics Project Descriptive Statistics PSYCH 625 Week 4 Individual Assignment Time to Practice – Week Four PSYCH 625 Week 4 Learning Team Assignment Statistics Project Comparing Means PSYCH 625 Week 5 Individual Assignment Programmatic Assessment Time to Practice – Week Five PSYCH 625 Week 5 Learning Team Assignment Statistics Project Correlations PSYCH 625 Week 6 Individual Assignment Overview of Important Statistical Tests PSYCH 625 Week 6 Learning Team Assignment Statistics Project Presentation ----------------------------------------- PSYCH 625 Week 1 Individual Assignment Basic Concepts in Statistics Worksheet For more classes visit www.snaptutorial.com Complete the following questions. Be specific and provide examples when relevant. Cite any sources consistent with APA guidelines. What are statistics and how are they used in the behavioral sciences? Your answer should be...
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...words the statistical analyses within the article. o Does the article incorporate graphs or tables that facilitate understanding of the data? o Are the descriptive statistical analyses appropriate for the subject? What descriptive statistics were used in the study? o Identify the inferential statistics used and comment if the analyses supported the research problem/hypothesis. (For example, do they support the conclusions reached by the author or authors? Are the statistics misleading or biased?). • The paper is 700 to 1,050 words in length. BSHS 435 WEEK 4 STATISTICAL ANALYSES • Student selected a peer reviewed article from the library related to human services and statistical analysis. • Student discussed statistical analyses, including the following information: • Summarize in 100 to 150 words what the research study discussed in the article is about. (Provide a complete citation for the article using proper APA format.) • Discuss in 250 to 400 words the statistical analyses within the article. o Does the article incorporate graphs or tables that facilitate understanding of the data? o Are the descriptive statistical analyses appropriate for the subject? What descriptive statistics were used in the study? o Identify the inferential statistics used...
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...Statistics in Business QNT/351 Aug 21, 2013 Edward Balian Statistics Investopedia defines statistics as a type of mathematical analysis involving the use of quantified representations, models and summaries for a given set of empirical data or real world observations. Statistical analysis involves the process of collecting and analyzing data and then summarizing the data into a numerical form. ("Investopedia", 2013) Types and Levels Descriptive statistics, inferential statistics, ratio-level data, interval- level data, ordinal-level data, and nominal-level date are some types and levels of statistics. Descriptive statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set, and to present the information in a convenient form. Inferential statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data. Business decision making When it comes to the role of statistics in business decision-making it is applied in many ways in terms of consumer preferences or even financial trends. For example, managers across any type of business formulate problems, they decide on a question relating to the problem and then form a statistical formulation of the question is used to determine answers to all of the above. An example of a business question may be how many calls are answered...
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...Additional Problem In order to explain the US defense budget, you are using the data from 1962 to 1981 with the following variables (all measured in billions USD) and estimate the corresponding model (Model 1):(Use α=0.05 for references) Yt: Defense budget outlay for year t X2t: GNP for year t X3t: US military sales in year t X4t: Aerospace industry sales in year t D1t: Dummy variable presenting the military conflict involving more than 100,000 troops; D1t=1 if more than 100,000 troops are involved and equal to 0 if fewer than 100,000 troops are involved. |Dependent Variable: Y Sample: 1962 1981 | |Method: Least Squares Included observations: 20 | |Variable |Coefficient |Std. Error |t-Statistic |Prob. | |C |21.40251 |1.496947 |14.29744 |0.0000 | |D1 |-48.21987 |6.871544 |-7.017328 |0.0000 | |X2 |0.013879 |0.003207 |4.328062 |0.0008 | |X3 |0.073146 |0.203805 |0.358902 |0.7254 | |X4 |1.389753 |0.130197 |10.67423 |0.0000 | |X4*D1 |1.540792 |0.325005 |4.740818 ...
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...price of Accenture from July 2001(the earliest available date) to September 2014 and that of 13-week Treasury Bill, as well as Fama French Benchmark Factors (Rm-Rf, SMB, HML) of the same time period. The data description is showed in Table 2, I then tested properties of those variables. 1. Normal Distribution The test statistics of histogram presented in Table 2 follows a chi-square distribution with 9 degrees of freedom. The critical value at 5% significance level is 23.6. So the results show that Rm-Rf and SMB are normally distributed; while RACN-Rf and HML are not normally distributed. 2. Correlation (Multicollinearity) The correlation matrix presented in Table 3 shows that the excess return of Accenture is positive correlated with the three factors. Positive correlation with SMB indicates that Accenture behaves more like a small stock. The positive correlation between independent variables indicates there may be problem of multicollinearity, which need further test. III. Single Index Model (CAPM) I first built the single index model: RACN-Rf=α+βRm-Rf+ε. The results are presented in Table 4. As a whole, the model is significant according to the F statistic. The intercept is 0.7919, which means when there is no market excess return, the excess return of Accenture is 0.7919. However, the intercept is not significant, thus statistically there’s no abnormal return of Accenture. β is 1.0971,...
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...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. * Standard deviation. Compute the standard deviation (σ) of the sampling distribution. σ = sqrt[ P * ( 1 - P ) / n ] where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size. * Test statistic. The test statistic is a z-score (z) defined by the following equation. z = (p - P) / σ where P is the hypothesized value of population...
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...Problem 1 Decision rule: Reject if tSTAT> 2.0096 d.f. = 49 Test statistic: Decision: Since tSTAT> 2.0096, reject . There is enough evidence to conclude that the mean number of days is different from 20. (b) The population distribution needs to be normal. (c) The boxplot plot indicates that the distribution is skewed to the right. (d) Even though the population distribution is probably not normally distributed, the result obtained in (a) should still be valid due to the Central Limit Theorem as a result of the relatively large sample size of 50. Problem 2 H0: = 1. The mean amount of paint is 1 gallon. H1: 1. The mean amount of paint differs from 1 gallon. Decision rule: Reject if |ZSTAT| > 2.5758 (a) Test statistic: cont. Decision: Since |ZSTAT| < 2.5758, do not reject . There is not enough evidence to conclude that the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is different from 1 gallon. (b) p-value = 0.0771. If the population mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon, the probability of obtaining a test statistic that is more than 1.7678 standard error units away from 0 is 0.0771. Problem 3 (a) Decision rule: Reject if |tSTAT| > 2.0555 d.f. = 26 Test statistic: Decision: Since |tSTAT| < 2.0555, do not reject . There is not enough evidence to conclude...
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...commonalities. E.g. intra/extra community for health and social services 3 Summarize 4 Compare 5 Inference/Interpretation II. Categorize Data 6 There are many ways to sort and categorize data e.g. demographically by age groups, by problem type 7 Geographic approaches may be used 8 Use of model; we are using the wheel from Neuman’s model. 9 Look for data convergence when categorizing-e.g. how many times do we see data converging in different categories? 10 Look for commonalties, health resources that are available. SEC, age, etc. III. Data Summary 11 Summary statements-summarize each table. 12 Summary statistics-put data into percentages and rates so that different areas/communities can be compared. Raw numbers will not work to compare different areas. 13 Graphic methods of data summary: 14 Remember that tables need concise summary data. P. 222, can put population statistics in graph. 15 Dependency Ratio: how many people in your community who can support the dependents. Calcuation on page 225. Should do for both census tracts. 16 Data summarization facilitates ease of reading and spotting trends/patterns in data IV. Summary Statistics 17 Rates-vital statistics 18 Percentages-population characteristics 19 Ratios-sex,...
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...Write a brief paper on Statistics and Operations Research in the context of Analytics. Analytics is defined as the scientific process of transforming data into insight for making better decisions. It is the combination of skills, technologies, applications and processes used by data scientist to gain insight in to their business based on data and statistics to drive business planning. It typically use’s data, statistical and quantitative analysis to measure the performance of the subject (Organization/ website etc.) on which a study is to be conducted. Analytics can be used in various fields such as market research, for studying user web pattern behavior & in many other applications to derive some meaningful information out of the complex world around us. But we will first touch upon the area of operations research & how Analytics with the help of various statistical tools can help to solve the operation related problem in an organization. Operations research overlaps with other disciplines, such as industrial engineering and operations management. It is often concerned with determining an optimal solution out of a business problem. It may either to maximize your profit, performance, or yield or minimize your losses, risk, or cost. In the fields of production, logistics, or sales where managers are facing a problems so as how to allocate resources, develop production schedules, manage the supply chain, and set prices. For example, it many help to decide how to organize...
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...Problem 1: i) All the coefficients are significant, because t (crit) = 1,96 is smaller than the absolute values of these three coefficients β1, β2 and β3. Estimated equation is: Log (wage) = 0.128 + 0.0904educ + 0.041exper – 0.000714exper2 (0.106) (0.0075) (0.0052) (0.000116) n = 526, R2 = 0.30 ii) Yes, the coefficient is significant because t-statistics absolute value 6,16 is greater than t (critical value) at 1 % significance level which is 2,586 in this case. iii) Return to the fifth year of experience: 100 * [0.041-2*(0.000714)*4] = 3,53% Return to the 20th year of experience: 100 * [0.041-2*(0.000714)*19] = 1,39% iv) x* = 0.0410089/(2*(-0.0007136)) = -28.7338 28.7338 There are 121 people in the sample with at least 29 years of experience. Problem 2: a) SSE + SSR = SST SST – SSE = SSR SSR = 7160,41429–10.6243285= 7149,79 b) n =524 c) R2 = SSE/SST = 10.62/7160.41 = 0,001484 d) t = (-0,4682478/0,5306473) = -0,88241 e) t = coefficient/ std. error coefficient / t = (5,944174/34,96) = 0,170028 f) F = t^2 = (-0,88241)^2 = 0,778645 Problem 3: Model 1: a) Coefficient on variable cigs indicates that one cigarette smoked per day reduces birth weight by 0,44 %. Therefore, the effect on birth weight from smoking 10 more cigarettes will be that it reduces birth weight by 4,4 %. b) In model 1, a white child is predicted to weight 5,5 % more than a non-white child on...
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...calculate the mean, median and standard deviation for the ounces in the bottles I first imported the data in excel. After importing the data I use the Data analysis function where I choose descriptive statistics. Once choosing descriptive statistics I clicked ok and input my data range. Afterward I selected summary statistics and press OK. The forwarding data was provided; the mean equaling 14.87, median equaling 14.8, standard deviation equaling 0.550. To construct a ninety-five confidence interval for the ounces in the bottles I use the following information. X equal to 14.87 which is the mean of the data from the bottles, n equal to 30, because of the amount of bottles we use, standard deviation equals zero point five five zero which was calculate with the data from the bottles. I use the formula [ ] which gave me the lower limit of 14.673 and an upper limit of 15.067. Finally I conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen ounces is supported. With the claim that the bottles contains less than sixteen ounces my null hypothesis is mean greater than equal to sixteen and my alternative hypothesis is mean less than sixteen. Using the formula [ ] I calculated that the value of the test statistic is negative eleven point two five three. With the critical value at the...
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