...J. Manning MA3110 Statistics Dr. P. A. Williams What is my meaning of Statistics? My meaning or definition of statistics is that of its base word itself. Stat. Along with other elements that would make it a definition or an opinion of sort, but I’m sure that I won’t be far from what others may say it means or what they think it means. Stat is defined as with no delay; at once. When most of us think about statistics, we think of comparisons, of two or more entities but ones balance might be more or less as well as winning and losing. There is still that scale that separates the two where one is ahead of the other. The people analyzing and drawing conclusions are getting this information have to get it out to those that follow up on whatever the subject may be fast because people want to know. It’s said that Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on data according to (Pearson’s Elementary Statistics Using Microsoft Excel by, Mario F. Triola). This is the same as I said without including all of the other tools needed, or used in Statistics. Television shows are another example being on statistic radar so to speak. You have so many television shows that are out right now, but how...
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...MA3110: Module 6 Correlation and Regression Exercise 6.1 Linear Correlation 1 In this exercise, you will solve three questions, where you will be asked to calculate a linear correlation coefficient and determine whether there is a linear correlation between the two given variables. Solve the following problems: Listed below are baseball team statistics, consisting of the proportions of wins and the result of this difference: Difference (number of runs scored) - (number of runs allowed). The statistics are from a recent year, and the teams are NY—Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City. Difference 163 55 –5 88 51 16 –214 Wins 0.599 0.537 0.531 0.481 0.494 0.506 0.383 o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics. Use α = 0.05. o Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference? A classic application of correlation involves the association between temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 minute and the corresponding temperatures in °F: Chirps in 1 Min 882 1188 1104 864 1200 1032 960 900 Temperature(°F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6 o Construct a scatter plot, find the value of the linear correlation coefficient...
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...Statistical Tool | Use/s | Level of Measurement | Formula | 1. Z – test | to determine whether two population means are different when the variances are known and the sample size is large. Source: http://www.investopedia.com/terms/z/z-test.asp#ixzz2LEqfeJnN | IV – NominalDV – Interval | | 2. T – test | to compare the means when the population mean is known but the population variance is unknown.Also when the population standard deviation is unknown but the sample standard deviation can be computed.Source:Basic Statistics Book | OrdinalInterval | | 3. F – test | used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled.Source:http://en.wikipedia.org/wiki/F-test | Ordinal Interval | | 4. Spearman rank | measures the strength of association between two ranked variablesSource:https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide.php | NominalOrdinal | | 5. Pearson R | used in the sciences as a measure of the strength of linear dependence between two variables.Source:http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient | Interval | | 6. Chi – square | to test the difference between an actual sample and another hypothetical or previously established distribution such as that which may be expected due to chance or probabilitycan also be used to test differences between...
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...the AIU data set in order to complete a regression analysis for benefits & intrinsic, benefits & extrinsic and benefit and overall job satisfaction. Plus giving an overview of these regressions along with what it would mean to a manager (AIU Online). Introduction Regression analysis can help us predict how the needs of a company are changing and where the greatest need will be. That allows companies to hire employees they need before they are needed so they are not caught in a lurch. Our regression analysis looks at comparing two factors only, an independent variable and dependent variable (Murembya, 2013). Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.018314784 R Square 0.000335431 The portion of the relations explained Adjusted R Square -0.009865228 by the line 0.00033% of relation is Standard Error 1.197079687 Linear. Observations 100 ANOVA df SS MS F Significance F Regression 1 0.04712176 0.047122 0.032883 0.856477174 Residual 98 140.4339782 1.433 Total 99 140.4811 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 4.731133588 1.580971255 2.992549 0.003501 1.593747586 7.86852 Intrinsic -slope 0.055997338 0.308801708 0.181338 0.856477 -0.5568096 0.668804 Line equation is benefits =4.73 + 0.0559 (intrinsic) ...
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...statistical analysis is descriptive analysis. Descriptive statistics can summarize responses from large numbers of respondents in a few simple statistics. When a sample is obtained, the sample descriptive statistics are used to make inferences about characteristics of the entire population of interests. Descriptive analysis is the transformation of data in a way that describes the basic characteristics such as tendency, distribution, and variables. A examples of this would be if a company wanted to find out what type of bonus employees prefer. Descriptive statistics are used to explain the basic properties of these variables. One descriptive statistics that is used to explain the basic properties of variables is Mean, Median, and Modes. These terms all would be descriptive statistics for the above example by describing the central tendency in different ways. The mean would reflect the average answer that is given. The Median would provide the answer that is the central or middle range answer. The mode would be the answer that was given the most often. A second descriptive statistic that is used to explain the basic properties of variables is Tabulation. This refers to the orderly arrangement of data in a table or other summary format. When the tabulation process is done by hand, the term tallying is used. Simple tabulation tells how frequently each response or bit of information occurs. A third descriptive statistic used to explain the basic properties of variables is Cross...
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...Hypothesis Testing – Two Sample * H0 : µ1 = µ2 H1 : µ1 ≠ µ2 * Case 1 -- If you know population variances, use this and Normal table * Case 2 -- If you know only sample variances, and samples are large, use this and Normal table * Case 3 -- If you know only sample variances, and samples are small, and unknown population variances can be assumed identical, use this and t-table, with n1 + n2 - 2 df. (sp is called “pooled estimate of σ”) * We use standard error of difference to compute (actual) t Hypothesis Testing – Means Of Dependent (Paired) Samples tActual * pooled estimate of population proportion Regression and Correlation Simple Linear Regression (Only 1 independent variable, and linear relationship) Regression Coefficients Using Method Of Least Squares, we get: Standard Error Of Estimate Correlation: * Variation of y around the regression line * Variation of y around its own mean * Coefficient of Determination Direct Computation of r: Chi-Square * Make working table as follows: * List observed frequency cells, fo , in 1st column. * Compute expected frequency, fe , for each cell, and write in 2nd column. * fe = RT*CT/n where RT = row total, CT = column total, n = total no of observations in all cells of data table. * Compute (fo – fe ) for each row of working table in column 3 * Compute...
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...TERM END EXAMINATIONS,MARCH-2013 BACHELOR OF COMMERCE, YEAR – III ELEMENTARY STASTISTICS Time: 3 hours M.Marks:60 SECTION A Note: - Attempt any 4 questions. All questions carry equal marks. (4 X 5) The answer should be limited upto 200 words. 1) What is statistics? Explain the nature and limitations of statistics? 2) What is frequency distribution? What are the different types of frequency distribution? 3) What is frequency curve? Explain cumulative frequency curve with example? 4) Suppose mean of a series of 5 item is30.four values are respectively, 10, 15, 30 and 35.estimate the missing 5th value of the series. ANSWER : Mean = (10+15+30+35+x)/5=30 Therefore, x=(30*50)-( 10+15+30+35) i.e x = 150-90, hence x=60 5) Calculate median of the following distribution of data. Class interval | 0-5 | 5-10 | 10-20 | 20-30 | 30-50 | 50-70 | 70-100 | frequency | 12 | 15 | 25 | 40 | 42 | 14 | 8 | n= 12+15+25+40+42+14+8=156 Hence median is at the average of n/2 & (n/2 +1) positon i.e 78th & 79th position Class interval | 0-5 | 5-10 | 10-20 | 20-30 | 30-50 | 50-70 | 70-100 | frequency | 12 | 15 | 25 | 40 | 42 | 14 | 8 | Position 12 27 52 92 134 148 156 6) Calculate the coefficient of correlation...
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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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...LLR 1st Quarter Report Project Name: Address: Project Manager: Area Manager: Staff Team: Volunteers: Contents 1. Introduction 2. Service Activity 3. Referrals 4. Outcomes 5. Engagement 6. Incidents 7. Feedback 8. Staff Development 9. Project Development 10. Conclusion 1. Introduction This report is based on the activities undertaken by ------- for the period between This initial introductory period has been a very successful initiation period in terms of the increasing number of referrals and assessments received and conducted, in addition to the rising number of service user (SU) engagements. During this reporting period, LLR inducted four new staff members who all completed LLR’s in-house training on the LLR, Health and Safety as well as File and Data Management training. Referrals over the few months have grown steadily with positive client engagement in groups, 1-2-1 counselling and 1-2-1 Recovery Plan Sessions. During this short period we have already observed an increasing number of SU’s being very committed to their recovery journey and we expect their commitment to be reflected in their continued growth and change. The staff and management team have also been very supportive and continue to provide us with regular group space ensuring group activities got underway. Although actual attendance numbers for the group have been relatively...
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...Research Design (Assignment 2) I will be conducting a study using a true experimental research design in order to investigate the effects of marijuana use on an individual’s problem solving ability. Marijuana use is the independent variable which is operationally defined as consumption in the form of smoking 0.5 grams of cannabis in a marijuana cigarette. Problem solving abilities is the dependent variable which is operationally defined as the total score on various math problems as well as time taken to complete said math problems. Scores on the math test can range from 0 to 100. 40 participants, 20 males and 20 females all of whom are 18 year old Freshmen taking Math 131 at Pasadena City College, will be utilized in this study. 10 males and 10 females will be randomly assigned to group A and will all smoke marijuana, while 10 males and 10 females will be randomly assigned to group B and will not smoke marijuana. In order to ensure that every participant in group A is affected by the marijuana equally, only students that consent to a drug test prior to the study and are found to have no traces of THC present in their blood will be eligible to participate in the study. This will ensure that all participants in group A are affected by marijuana equally by eliminating the possibility of one participant having a higher tolerance than another. In order to eliminate all possible plausible alternative explanations for the relationship observed between marijuana use and problem solving...
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...What elements should be considered when buying a home? Does the age of the home make a difference in the price? What about the square feet of the home? Does having a house with more square feet mean that the price of the home will increase? Well my fiancé and I are looking to buy a home and have come to the conclusion of five factors that we think are the most important. Using statistics, we will narrow our search down from 108 homes to only a few homes. The first thing, we need to discuss is the dependent and independent variables. Since we are most concerned with the price of the home and how other factors affect it, we will use PRICE as the dependent variable. We have other factors that influence the price such as square feet (home size), number of bedrooms, number of bathrooms, heat (gas forced or electric), style (ranch, two floor, or tri-level), garage, basement, fireplace, age of the home, and the school district which will be our independent variables. Out of these, we have decided to pay close attention to the square feet (home size of 1900 square feet or more), number of bathrooms (3 or more), heat (gas forced), basement, and the age of the home (less than or equal to 10 years). We chose these factors because we wanted to know what kind of relationship, if any, they have with the price of the home. To figure that out, we will be doing a series of tests to discuss the price difference for the independent variables. Then we will get the probability and confidence...
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...Process Improvement Plan Jennifer DeRosa OPS/571 October 3, 2011 Tonya Webster PMP, CSM Process Improvement Plan Statistical Process Control is a technique that can be used to test output from a process. It is useful in determining how a process is currently being performed and if it can be improved upon (Chase, Jacobs, & Aquilano, 2006). As part of my week one assignment, I created a flowchart that detailed my weekday morning process. I chose this process because I wanted to find ways to reduce the amount of time it took me to get the kids off to school. By creating a flowchart, bottlenecks were identified as well as opportunities to maximize the limited amount of time I have to complete my morning routine. This paper will again use the process identified in week one to complete a Statistical Process Control that can be used to verify my standard process is operating in a way that allows me to complete all of the tasks and affords me additional time. This paper will also outline the control limits of my morning process, the effects of any seasonal factors, and the confidence intervals involved. Statistical Process Control Data was recorded for a period of two weeks on how long it took me to complete my morning routine and get my kids off to school. I tracked the minutes it took me to complete each step of my morning routine and used the totals from each day to calculate the mean. On average, the time it took me from the time I woke up to...
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... Lynne s Background (Why me?) Lynne’s Background (Why me?) • 40+ years in industry – Nabisco, then Kraft , – Unilever (Lipton) – Hunt‐Wesson Foods • Academic – AB Math The Colorado AB Math, The Colorado College – MS, Applied and Mathematical Statistics, Rutgers – PhD, Interdisciplinary, Rutgers • Government: NIST Government: NIST • Academia – Cal. St. Fullerton (MBAs) – Rutgers (Experiment Station) ( ) • ASA – Chair P&Q Division – Fellow ‘94 • Consulting – Consumer goods – Pharmaceuticals – R&D, Manufacturing, Quality • ASQ – Chair Statistics Division – Fellow ’86 – Column Quality Progress Column: Quality Progress Slide 3 Statisticians?? Not sure N t Yes No Don’t care. This is the only session that looked remotely interesting. that looked remotely interesting 4 How can you tell? How can you tell? • If you have more than one pen with you If you have more than one pen with you • If you know more than one joke about the binomial distribution binomial distribution • If your glasses are thicker than mine • If you are too shy to be an accountant • If you talk to your colleagues in SAS y y g 5 1. Motivation 1 Motivation Statistical Engineering 1. Motivation The State of Statistics as...
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...Portfolio Analytics 1. Introduction: To analyze our portfolio and determine its exposure to risk factors, we assumed that: Rit+1=a+bi,1F1t+bi,2F2t+…+bi,nFnt+eit+1 First, we calculated z-score for logarithm of b_p and logarithm of cap to determine sensitivities for stock-specific factors. After we got all 13 sensitivities, we did a weighted regression of the 13 sensitivities against the 1000 stock’s forward return in 60 periods, respectively. For each period, we got 13 coefficients, which were the risk premiums for each risk factor. Finally, we regressed the risk premium from our regression against the portfolio return, bench return and active return. Doing so, we get these returns’ sensitivities against risk factors and were able to determine our portfolio’s exposure to various risk factors. 2. Procedures and Analysis 2.1. Working Procedure Nearly all of the calculations in part II were done by VBA Macros. In the Project part2.xlsm, there were 6 worksheets. The Data recorded all the cross-sectional data for 60 periods, having 1000 stocks in each period. StockPriceData recorded the data for stocks in our portfolio. To run the regression, we assumed that for a particular stock, the forward return in a particular period was, rt+1=bisec10λsec10+…+bisec55λsec55+bibetaλbeta+bilnbpλlnbp+bilncpλlncp+e . The equation has no intercept, the risk premium for sector factor has already included the zero beta rate. To prevent stocks with smaller market capitalization...
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...Problem 1 A random sample of 16 adult males is about to get into an elevator which has a weight capacity of 2900 lbs. The adult male weight follows the normal distribution with a mean of 170 lbs and a standard deviation of 15 lbs. (a) What is the probability that the total weight for this sample of 16 adult males will exceed 2900 lbs? Hint: This is the same as calculating the probability that the average weight for a random sample of 16 exceeds 2900/16. (b) Will the probability calculated above apply if 16 members from the Blue Hens football team were to get onto the same elevator? Why or why not? (c) 95% of average weights in a random sample of 16 adult males will exceed _______ ? ==================================================== Problem 2 The adult male height follows the normal distribution with a mean of 70 inches, and a standard deviation of 4 inches. (a) What is the probability that an individual male selected at random is more than 74 inches tall? (b) What is the probability that the average height for a group of 4 randomly selected males exceeds 74 inches? (c) Why are the answers to parts (a) and (b) different? How large of a random sample would we need to reduce the standard error to 0.25 inches? Problem 3 Historical data suggests that the proportion of left handed people is between 7 to 10%. We decide to take a random sample of people to confirm this. (a) How large would our sample...
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