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Statistical Theory

Statistical theory is a very general concept which serves to elucidate the origin of other statistical practices. For example, the practices of statistical inference, mathematical statistics, probability and statistical decision-making, are all based from the framework of statistical theory.

Furthermore, the study designs and data analyses practiced by researchers and statisticians are techniques which satisfy the principles of statistical theory. Similarly, comparisons can be generated between data sets because statistical theory provides the necessary guide required for comparing data. Evidently, statistical theory is a part of all areas of statistics which involve analyzing, describing, and using data to create conclusions and formulate future decisions. 

Statistical theory provides the rationale for the full range of steps involved in statistical analyses. The techniques of modelling, data collection, summarising data and interpreting data are all based from statistical theory. For example, in terms of summarising data, the principles of statistical theory account for the different ways which data can be summarised and which aspects of the data should be summarized. Additionally, statistical theory addresses how well a limited sample size can describe a data set.

Clearly, in the study of statistics, statistical theory has many applications and therefore, allows statistics to extend beyond pure mathematics and connect research with the real world. It is through statistical theory that predictions and/or conclusions can be made from data sets, which is the general objective of statistical inference. Furthermore, it allows researchers to attempt to answer problems and explain cause-and-effect phenomena. Thus, it is also linked to the subjects of Bayesian inference and general estimation. 

Categories within Statistical Theory

Spearman rank correlation coefficient by Messina

1) Write a paper (750-1,000 words) regarding the use of the Spearman rank correlation coefficient by Messina, et al. in "The Relationship between Patient Satisfaction and Inpatient Admissions Across Teaching and Nonteaching Hospitals," listed in the module readings. 2) Comment on what variables were used; whether it answered th

Regression Models

[1] The data in DJIA.xls represent the closing values of the Dow Jones Industrial Average (DJIA) from 1979 through 2008. a) Plot the time series. b) Find a three-years moving average to the data and plot the results. c) Using a smoothing coefficient of W= 0.30, exponentially smooth the series and plot the results. [2] R

T-Test - Applied Statistics for Psychology

MM570 Applied Statistics for Psychology Unit 6 Project: Descriptive Statistics Review Sheet Place all answers, work, and graphs in this document. Use alpha = .05 for all hypothesis testing questions. ** Please use non-directional two-tailed tests for these questions (not one-tailed tests). **All SPSS output must be sh

EconomicSTATS and Forecast Function

See the attached files. 1. Using regression analysis, (i.e. do not use the forecast function in Excel) forecast the average annual consumption of natural gas for each group in 2014. That is, how much natural gas is consumed during an average month? How confident would you be in concluding the coefficient estimates are not

Financial Advisement: Regaining Stocks

Assume the financing gurus of a weekend investment television program predicted a 50% chance of XYZ stock gaining in January and a 50% chance of gaining in February. Your financial advisor sees this and tells you there is a 100% chance XYZ stock will gain over the 2-month period. Would you continue to use this financial advisor?

Air Force Training Program

This is an analytic review that needs to be done using the data computed in minitab. The guidlines for the review and the problem have been uploaded as well 1) Use Minitab software to generate the output used in your analysis. The file containing the problem data, <AIRFORCE.MTW 2) You are expected to folow the report form

Decision theory: optimal solution and conditional probability

Stochastic Operations Research Read: Sections 12.3 - 12.5, 13.1, 13.4-13.6 in "Winston, Operations Research: Application and Algorithms, 4th edition, 2004, Thompson, ISBN 0-534-38058-1." Question 1 Diamond and Forrester (1979) applied Bayes' rule to the diagnosis of coronary artery disease. A procedure called cardiac fl

Sampling Distribution and Population Distribution

I assume my scenario will have to include enough information to answer the questions below so I will need help with this one as well Create and write your own scenario about a specific population. Then, answer the following questions about your scenario: What are the mean, standard deviation, and shape of the population d

Probability distributions - normal distribution

1. What percentage of the area under the normal curve lies a. To the left of the mean? b. Between μ - 2σ and μ + 2σ? c. More than three standard deviations above the mean? 2. Over an entire summer, an amusement park gets an average of 21.7 people per day that have to go to the infirmary. Some days it is higher than

Z-Scores and Extreme Scores

Please explain how I set up and solve this problem: For each of the populations would a score of x= 50 be considered a central score (near the middle of the distribution) or an extreme score (far out of the tail of the distribution ) is this set up x-u/o? u=45 o= 10 u=45 o= 2 u= 90 o= 20 u= 60 o=20 If i have a proble

spss

12. A college using a new method of teaching calculus wishes to evaluate the effectiveness of the method. A class of 24 first-year college students was randomly divided into two sections, one of which was taught using the new method and the other taught using the old method. Scores on the end-of-semester exam for the two groups

Normally Distribututed Data

Please help with this multi-part question on statistics: The YUMM cereal company distributes Colored Sugar Cereal. Each box is supposed to contain 450 grams of cereal. They also sell cereal in a "2-pack," where each "2-pack" contains 2 boxes of cereal. The 2-packs are supposed to have a total weight of 900 grams. YUMM can choo

need assistance to figure this out

You have taken data from a production process in order to develop an Xbar control chart. You have 25 samples of data with 5 parts measured in each sample to get the Xbar and R (Range). Use this data shown in the table. Sample 1 2 3 4 5 Xbar R 1 1.55 1.58 1.64 1.67 1.50 1.588 0.17 2 1.52 1.62 1.71 1.74 1.60 3 1.47 1.5

Random Sampling - statistics

Doctors identify "chronic tension-type headaches" as headaches that occur almost daily for at least six months. Can antidepressant medications or stress management training reduce the number and severity of these headaches? Are both together more effective than either one alone? The research design necessitates the creation of 4

Calculating the Confidence Interval for Standard Deviation

In manufacturing tablets, the quantity of active ingredient that is required to lie within 5 mg of the mean is normally distributed and the required condition is considered to hold if sigma < 1.6. A sample of 35 tablets has a sample standard deviation s = 1.321 (a) Find a 95% confidence interval for sigma. (b) Formulate and pe

Calculate Z scores for the depenent and independent variable

Calculate Z scores for the dependent and independent variable values in the two hypotheses below. This will require calculating the standard deviation and converting the scores to Z scores. Hypothesis: 1 (population per 100,000 ROBBERY ARRESTS CONVICT

Six Sigma Project

Please use information provide on step 1 and 2 to resolve steps 3, 4, 5. 3) Define Phase Based on the problems identified on step two I need a Project Scope Statement and a SIPOC. 4) Repeatability and Reproducibility System Report showing what data must you collect? Who will collect the data? How do you trust that the d

Inferential Statistics and Point Estimate

Suppose a confidence level is 0.44 < p < 0.60 What is the value of the point estimate p-hat (round to nearest hundredth) What is the margin of error E= (round to the nearest hundredth)

Mixed Data and Statistics Questions

1. What is the differences between statistics as numerical facts and statistics as a discipline or field of study. 5. Consider the data set for the sample of 10 minisystems in Table 1.7 a. how many variables are in the data set? b. Which of the variables are quantitative and which are qualitative? c. Which is the average C

Conditional Expectation

P(x1,x2)= (x1 choose x2) (1/2)^x1 (x1/15), x2= 0,1,2, ...., x1 x1= 1, 2, 3, 4 ,5 0 elsewhere is the joint pmf of X1 and X2. Determine E(X2|x1)

Indicator function and ancillary stats

7.9.1 Let Y1<Y2<Y3<Y4 denote the order statistics of a random sample of size n=4 from a distribution having pdf f(x;&#952;)= 1/&#952;, 0<x<&#952;, zero elsewhere, where 0<&#952;<infinity. Show that the pdf is of the form 1/&#952; f(x/&#952;), where f(w)=1, 0<w<1, zero elsewhere. Please see attached for full question.

Distribution of Y

Let X1, X2,...,Xn denote a random sample from a distribution that is N(&#956;, &#952;), 0<&#952;<infinity, where &#956; is unknown. Let Y = the sum from 1 to n of (Xi-Xbar)^2/n=V. What are the E[Y] and Var[Y].>0. Please see attachment.

Order Statistics-Determine the E(Yn) and V(Yn)

Let Y1<Y2<.....<Yn denote the order statistics of a random sample of size n from a uniform distribution on [0, theta] ie) f(x)=1/theta if 0<x<theta, 0 otherwise, where theta>0. Determine the E(Yn) and V(Yn).

Estimation is examined.

"Hockey-r-us," a store specializing in sales of hockey equipment, wants to find out the average age of all its customers. A random sample of 25 customers reveals an average age of 38 years with a standard deviation of six years. It determines a 95% confidence interval of the average age of all customers.

Statistics - Data Models Topic

10) Clearly define the decision variables, the objective function and each constraint. From the Solver Solution, include the value of objective function and each of the decision variables.