...: β = β0 ˆ We proceed by estimating β. We denote the estimated value as β. This could for example be a sample mean estimate of the population mean, a least squared estimate of a regression coefficient, or a maximum likelihood estimate of a model coefficient, ˆ depending on the context. The estimate β is usually accompanied by a standard error ˆ to indicate how precisely it is estimated. We denote this standard error as se(β). This ˆ is a random variable with a sampling distribution. It will have reflects the fact the β different values in different samples. We can then form the following test statistic by computing the standardised statistic ˆ whereby we subtract the hypothesisized value β0 from the estimate β and divide by its standard error: t-stat = ˆ β − β0 ˆ se(β) ˆ Again, this test statistic is a random variable since it depends on β, which is itself a random variable. To make inference and do hypothesis testing about the value of β, we must assume a distribution for the above test statistic. This distribution is based on the null hypothesis being true. Since, for an unbiased estimate, the test statistic has zero mean and is standardised by its standard error, the test statistic doesn’t depend on the 1 units of β,...
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...the New York Mets, have strong numbers but the Phillies came out on top when comparing both data sets. The Phillies have a mean number of wins at 79.72 and the Mets with a mean of 77.28 wins. So, by looking at these data sets from a comparative angle, the Phillies come out on top with an average of about 2-3 wins per season. Taking a look at the medians, you are able to see that Phillies also have a higher mean of 80.5 wins as opposed to the Mets’ 78 wins. By looking at the easy to find statistical values you are able to see which team has been statistically better throughout the past 45 years. After I took a look at the descriptive statistics I ran three different tests: the F-test, the t-test, and the empirical tests to test for each data set’s normality. The first test that I ran in Excel was the F-test, which is a test comparing statistical models to identify the model that best fits the population from which the data was sampled. My results of the F-test came out with a high variance for each team: the Phillies with 133.41 and the Mets with 220.21. The reason for this is most likely based on the fact that there is a wide range of win numbers throughout the years. Wins from the Phillies have a range of 47 and the Mets have a wider range of 67. The degrees of freedom are at 90 which is found by adding the number of observations in each data set and subtracting 2. Continuing, the F-Stat was calculated to be approximately .60583 and...
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...Variables in our modern world effecting University Students’ academic success Abstract This research investigates the factors and variables that affect students’ academic results. This research paper focuses on variables which include hours of work, gender, high School academic results, hours of study and what relationship it has with our dependent variable which is the GPA. We aim to discover what relationship our variables hold with the dependent variable; if it is significant or in significant to be able to determine if it is valid to be rejected or accepted in our model. This study will draw upon the raw data that has been collected by surveying 50 university students from the University of Western Sydney. We have provided students with a questionnaire for numerical and measurable data related to the variables. Our data is validated and reiterated by previous literature, and we have created our own questionnaire which collects academic data where GPA is influenced highly by the selected variables. Our research is presented using a cross section data with many subjects without regard to difference in times. The data is uploaded on an excel spread sheet and ran through a STATA program to allow us to see the significance and correlating levels. The findings of this research is deemed to be a great source of knowledge for education institutions, students and the government to be able to further understand what major factors affect a student’s results. These results could...
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...this assignment. Write a three to five (3-5) page paper in which you: 1.Compare and contrast the comprehensive annual financial report (CAFR) of the selected local government entity with the city of Austin report from Week 1 homework. In your comparison, include: a.Publication method of the CAFR b.Audit and budget information in the CAFR c.The type of audit report issued d.Existence or non-existence of an internal audit function within the government entity 2.Prepare the analysis for the selected local government entity, including information on the introduction, financial section, and statistical section prepared in the city of Austin’s CAFR from chapter 2. 3.Analyze the methods used by the selected local government entity in comparing the budget-to-actual reports. Your analysis should include an evaluation of the basis of accounting used for the budget and financial statements. 4.Analyze the sources of revenue on the selected local government. Your analysis should include information on both governmental and business-type activities of the government. In your report, be sure to examine a.Property taxes and how they are...
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...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) Intercept- t-stat HO: Coefficients is zero. Intrinsic t-stat is zero...
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...Michael Jordan vs LeBron James This is one of the most controversial topics in the history of NBA today. I will finally put to rest all of the doubt that Michael Jordan is, was, and will always be the best player ever to play in the NBA. I know I sound bias but everyone in the world is comparing LeBron James to Michael Jordan. There are many similar traits about the two players but there are also many differences. I will cover as many as possible in both areas about both players and once you read the facts you will finally understand why Jordan is the King not James. Michael Jordan started his basketball career when he went to the University of North Carolina. While attending college he won a national championship and cemented that he was a great college player. Jordan was drafted into the League in 1984 and from there the rest is history. Michael Jordan was a Six-time NBA champion (1991-93, 1996-98); NBA MVP (1988, '91, '92, '96, '98); 10-time All-NBA First Team (1987-93, 1996-98); All-NBA Second Team (1985); Defensive Player of the Year (1988); Nine-time All-Defensive First Team (1988-93, 1996-98); Rookie of the Year (1985); 14-time All-Star; All-Star MVP (1988, '96, '98); Two-time Olympic gold medalist (1984, '92). He was also the all-time leader for average points per game with 30.1. LeBron James was drafted into the league straight out of high school in 2004. He has played in the NBA for ten years and for two teams. LeBron is a three-time NBA regular...
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...compare two athletes. I will compare and contrast the NBA players, Lebron James and Kobe Bryant. 2) Why have you chosen these two topics? Explain. I’ve chosen to write about Kobe Bryant and Lebron James because I feel that I will get more information about these two NBA players. They are both some well-skilled players that teenagers love even myself. 3) Which pattern of organization do you plan to use in your essay? Why? In the essay the first two will be background information stats. The rest of the essay will be comparing and contrast because you can really see the differences between these two outstanding players. 4) Which criteria do you plan to use in your essay? (AT LEAST FOUR) a. Background Information b. Stats c. Strengths and weaknesses on the court d. Training and work ethnic 5) Below, write a rough draft of your thesis sentence for this essay. Although Kobe and Lebron are different in many ways, they can compare in Stats and greatness. 6) Conduct some preliminary research, and write the Works Cited citations for TWO websites that you could use for this assignment. Lebron became an immediate NBA star player, skipped college school and joined the Cleveland cavaliers straight out of high school. He led the Miami Heat to the championship two times in a row. (www.biography.com) Kobe skipped high school to join the NBA. Kobe pocketed 3 rings by his 24th birthday and was a best all-around player....
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...making your decisions on rejecting or not rejecting the null hypothesis. 1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value -- see column S) Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries? Males Females Ho: Mean salary = 45 Ho: Mean salary = 45 Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us. Male Ho Female Ho Mean 52 45 Mean 38 45 Variance 316 0 Variance 334.667 0 Observations 25 25 Observations 25 25 Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 df 24 df 24 t Stat 1.96890383 t Stat -1.9132...
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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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...Plant Competition INTRODUCTION This experiment was used to show the different types of competition between species. Competition was defined as being a “relationship between members of the same or different species in which individuals are adversely affected by those having the same living requirements, such as food or space” (Competition 2010). There are two different types of competition that we will be observing during this experiment. The first type would be intraspecific, which means “competition between same species” (1976). The second type of competition is interspecific, which is defined as “competition between different species” (1976). These two types of competition have helped us look at the different types of interactions between plants species. The lab manual says that intraspecific competition experienced in plants is often very intensely prevalent, and the interspecific competition has the potential to be, mainly because they use most of the same resources (2015). For the experiment conducted for this report, intraspecific and interspecific competition was looked at using numerous set ups of radish and bean plants, and measured through the leaf length and biomass of each particular pot planted. The hypothesis that was fomred was that there would be intraspecific competition occurring between the radishes when planted in low density and high density, as well as intraspecific competition occurring between the beans planted in low density and high density, and...
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...Week 4 Reflection Jennifer Wood Week 4 Reflection When comparing two or more groups there are five tests that are used: Standard T-Test, Paired T-Test, One-Way ANOVA, Two-Way ANOVA, and Linear Regression. The Standard T-Test is the most basic testing when you are comparing the means of exactly two groups. A Paired T-Test is more used in a “Before vs. After” experiment, and is the most sensitive test out of all five. One-Way ANOVA test is just like the T-Test except you can use this test for comparing three or more groups. The Two-Way ANOVA test can be used when comparing three or more groups, which have two different independent variables. According to “Statistical Testing For Dummies!!!" (n.d.), “the Linear Regression test is for comparing the means of groups along a continuum of three or more treatment levels, such as a gradually increasing depth of water” (para. 16). References Statistical Testing for Dummies!!!. (n.d.). Retrieved from http://www.cbgs.k12.va.us/cbgs-document/research/Stats%20For%20Dummies.pdf Footnotes 1[Add footnotes, if any, on their own page following references. For APA formatting requirements, it’s easy to just type your own footnote references and notes. To format a footnote reference, select the number and then, on the Home tab, in the Styles gallery, click Footnote Reference. The body of a footnote, such as this example, uses the Normal text style. (Note: If you delete this sample footnote, don’t forget to delete its in-text reference as...
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...Huffman Trucking Driver’s Log Database Jules Mohr University of Phoenix BSA/310 Business Systems Facilitator: Heather Farnsworth January 22, 2010 Huffman Trucking Driver’s Log Database In this document I will describe the information database that Huffman Trucking uses for their Driver’s Log. The uses and significance of this database are varied including a list of drivers and their records of contact information as well as trip statistics and any moving violations. The Driver’s Log Database is necessary to Huffman Trucking business operations because it allows comparative analysis of driver's violations and trips. The Driver’s Log Database was written for Huffman Trucking by Smith System’s Consulting. This log contains the information for the entire contingent of driver’s employed by the company. The information is input by administrative personnel from interviews with and paper logs kept by the drivers. This database is divided into three disparate sections. The driver’s information section has contact, license, emergency contact, physical, and drug test information on each driver. The Driving Log holds the statistics from each trip. This includes driver information, co-driver information, driving times, sleeping berth times, on duty stop times, off duty time, trailer information, and odometer information. The violations log has the driver’s information as well as the date, state, description, status, and disposition of the violation along with...
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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 statistics...
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...also impossible to ignore the creation of the World Wide Web in 1995, with its radical growth from sixteen million users in 1995, to three thousand and seventy-nine million in December 2014 (cf. Internet World Stats 2015). The internet is changing the daily life of individuals in areas such as shopping, job hunting...
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...of the outcome. Probability is tool of measurement used to determine the likelihood of an occurrence during an event. Because people are often challenged with uncertainty when making a decision the probability concept is important in the decision making process. Statistics are used for probability analysis of events that cannot be controlled. Many decisions are often made with a significant lack of knowledge and probability helps to determine the unknown. Further, when comparing several alternatives it is often difficult to make a decision regarding which alternative to choose. Making a decision is very similar to a gamble. To determine the consequence of a decision the value of an outcome and its probability must be calculated. Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating conditional probabilities (Stat Trek, 2013). In applying Bayes’ theorem one must recognize the types of problems that only can be used. The following conditions must exist in considering Bayes’ theorem (Stat Trek, 2013): ■ The sample space is partitioned into a set of mutually exclusive events { A1, A2, . . . , An }. ■ Within the sample space, there exists an event B, for which P(B) > 0. ■ The analytical goal is to compute a conditional probability of the form: P( Ak | B ). ■ You know at least one of the two sets of probabilities described below. • P( Ak ∩ B ) for each Ak • P( Ak ) and P( B | Ak ) for each Ak For example, Bob is building a deck tomorrow. The weather...
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