**STATISTICS TUTORIAL CENTER AND LIBRARY**

**SANTA ROSA JUNIOR COLLEGE **

**AND **

**SONOMA STATE UNIVERSITY**

**Another Learning Resource from PerfectDisplay.com **... Serving Santa Rosa California and the World Beyond

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The Santa Rosa Statistics Tutorial Center and Library, is an online reference to statistics problems with solutions for those studying elementary college level statistics. It is used to supplement the statistics tutoring I provide for Santa Rosa and Sonoma State students.

Hundreds of solved problems are included that cover the complete range of topics covered in elementary statistics courses. Started on May 31, 2010, the reference is to be organized so that you can find problems by specific statistics topics. The first section focuses on general statistics used for the creation of statistical charts such as histograms.

The overall structure of the reference material focuses on the core of elementary statistics, using the z-test and t-test formulas to find z test statistics, t test statistics related to both the population mean and the population proportion. The z test and t test problems are also organized to provide a concrete understanding of how to calculate the confidence intervals for the mean and the proportion for problems involving one mean, one proportion and difference between two means and two proportions.

**STATSITICS CHARTS, GRAPHS AND PLOTS**

- GENERAL CONCEPTS
- CHARTS, PLOTS AND TABLES USED IN STATISTICS
- FREQUENCY DISTRIBUTION TABLES AND HISTOGRAMS
- BAR CHARTS
- STEM AND LEAF CHARTS
- BOX PLOTS
- REVIEW AND FORMULA SHEET
- MULTIPLE CHOICE TEST WITH ANSWERS

**GENERAL STATISTICS CONCEPTS, MEASUREMENT OF SCALE, DESCRIPTIVE AND INFERENTIAL STATISTICS, TERMS AND DEFINITONS**

- What is the difference between ordinal, interval and ratio variables? Provides a concise and comparative analysis for the classification of statistics variables.
**Rating A** - Statistics Discusses the basic terms and variables used in statistics. Includes an explanation of measurement scale variables which includes nominal, ordinal, interval and ratio.
- Link Outdated: Introduction to Measurement and Statistics Defines inferential and descriptive statistics. Includes measurement variables.
- Elementary Concepts in Statistics Discusses the elementary concepts related to statistics, Such as inferential and descriptive statistics and measurement variables.
- Types of Variables
- Introduction to Basic Statistics, Histograms, Measures of Tendency
- Mean, Mode, Median, and Standard Deviation
- Mean and Standard Deviation for Grouped Data
- Sampling and Statistics
- Measures of Central Tendency A few sample questions with answers and hints. Provides easy to use interactive tools that reinforce the learning process.
- Principle of Proportionality
- General Questions and Solutions Statistics questions related to population parameters and sample statistics.
- Scales of measurement Questions and Solutions related to scale of measurement: ordinal, ratio, variables.
- Summary statistics includes 41`multiple choice questions and solutions related to mean and modal number, measure of central tendency. determination of mean, median, standard deviation and highest value, shape of a histogram, skewed distributions, frequency distribution, class mark, grouped data, relatively frequency distribution, percentile determination.
- Percentiles includes 5 multiple choice Questions and Solutions for percentile problems.
- Empirical rule questions and solutions
- Experimental and survey design: Questions and Solutions
- Expected values questions and solutions .
- General: questions and solutions.
- Sample Proportions and Point Estimation (point esitmates of the mean)
- Sampling Distributions: Questions and Solutions
- Practice Problems for Section One Above Includes 15 problems with explained solutions.

**CHARTS, PLOTS AND TABLES USED IN STATISTICS**

Overview of Different Types of Charts and Tables Used in Statistics

**FREQUENCY DISTRIBUTION TABLES AND HISTOGRAMS**

- Frequency Distribution Tables and Histograms Sample problem constructs a frequency table distribution and then constructs a histogram from that table.
- Steps for Generating a Histogram, Representation of Statistical Data
- Histograms and Histographs
- The Histogram
- Histogram Example Based on Commute Time Offers different methods to calculate the interval width, also known as the class size or bin width. Several different methods are presented, even though there is no one way that is considered best for de terming the bin width.
- Histograms: Construction, Analysis and Understanding Illustrates the construction of a basic histogram. Concepts for determining median, mean and standard deviation from histogram.
- Histogram Interactive Tool Tool lets you set interval width, enter data or use given data and generate histogram plot.
- Making a Histogram - An Example that evaluates the bin size or class size for a histogram and its effect on the data representation.
- Histogram Multiple Choice Problem, Associating Frequency Distribution Table with a Histogram
- Constructing a Histogram
- Skewed Right Histogram
- Right Skew and Left Skew of a Histogram
- Skew of a Histogram: Relationship between left and right skew and position of mean and median in relation to each other.
- Histograms and other plots questions and solutions . Gives several problems with answers on histograms, scatter plots, box plots as related to median, mean, standard deviation, and percentile.

**BAR CHARTS **

**STEM AND LEAF PLOTS**

Step to make a stem plot from a frequency distribution table. Gives 5 problems with complete solutions.**Stem-and-Leaf Plots**- StemPlot Introduction to stem plots. Stem plots explained with an example problem that shows the complete steps to analyze a stem plot.
- Descriptive Statistics and Stem and Leaf Diagrams

**BOX PLOTS**

- Box Plots Visual Demonstration Relation to the Normal Distribution Curve. Interquartile Ranges, Mean, Median Location on Box Plot.
- Percentiles and Box Plots

**PROBABILITY INTRODUCTION**

- What Is Probability?
- Intuitive Probability
- Introductory Probability Problems with Solutions. Includes 9 basic probability problems with detailed solutions. Also 5 exercises with answers are included.
- Probability Problem
- Importance of Having Sample Space Defined
- Probabilities
- Proofreading Example
- Geometric Probabilities

**PERMUTATIONS AND COMBINATIONS**

- Discussion of Permutations and their meaning with problems. Gives permutation problems with solutions along with exercises.
- Introduction to Combinations with Example Problems and Solutions. Includes about 20 combination problems with solutions and exercises. Many of the problems focus on use of the combination formula. However others will give you, along with the overview, the ability to discern when to use the permutation and when to use the combination formulas.
- Introductory Permutation and Combination Problems. Includes 5 permutation and combination problems with explanations.
- Basic Permutation and Combination Problems. Basically a good set of 8 basic problems that you see often. Comes with complete solutions.
- Combinations and Permutations. 8 combination and permutation problems with solutions. Also includes 8 exercises with answers. The problem set emphasizes the permutations are basically the number of ways you can arrange a group of objects. Combinations on the other hand are referred to problems that require a selection of objects, that is how many ways can you select a given number of objects from a group of objects where order doesn't;'t matter, 123 and 321 are the same when dealing with a combination.
- Problem Solving with Combinations. A flow chart to determine whether or not you should use the permutation or a combination formula. Includes 4 worked examples problems with solutions.
- Difference Between Combinations and Permutations

**TREE DIAGRAMS AND PROBABILITY**

- Tree Diagrams and Probability - Several tree diagram probability problems with solutions. Sampling with replacement and sampling without replacement.
- Tree Diagram Problems With Replacement and WithOut Replacement. Provides 14 tree diagram problems with solutions. The first examples and problems use a tree diagram to find the probability without replacement and the second set uses a tree diagram to find the probability without replacement. A urn of 11 balls is used with 8 blue balls and 3 red balls as the general example. All probabilities for every combination is found. There are 121 possible ways to select.
- Trees and Counting

**CONDITIONAL PROBABILITY**

- Probability and Independence
- Mutually (Jointly) Independent Event
- Independent Events and Independent Experiments
- Dependent and Independent Events
- Conditional Probability and Independent Events
- Conditional Probability
- Conditional Probability. 5 basic conditional probability problems are given with solutions. Also 5 test problems are given.
- Conditional probability as explained by Wikipedia. A more advanced explanation is given in terms of Bayes theorem. The classical doctor patient conditional probability problem is given and solved. This problem related to the probability of a false positive and a false negative for the the determination if a patient has a disease.
- Bayes' Theorem

**RANDOM VARIABLES AND SAMPLE SPACES **

- Continuous Sample Spaces
- Discrete Random Variables: Example Problems with complete solutions. Expected Values, Poisson Random Discrete Variables, Hypergeometric Discrete Random Variables, Binomial Random Discrete Variables
- Random Variables, Discrete Random Variables, Continuo's Random Variables, -Variable.aspx Includes definition of random variables and two worked example problems.
- Random Variable Glossary Definition
- Discrete Random Variables Heads and Tails Analogy, Complex Die Example, Worked,
- Sample Spaces and Random Variables Illustrates the sample space from tossing coins and rolling dice. Discusses finite sample space and infinite sample space also.
- Random Walks
- Algebra of Random Variables
- Advanced Mathematical Discussion of Random Variables

**PROBABILITY DISTRIBUTIONS**

- Probability Distributions Introduction to probability distributions. Includes worked example sample problems, level I. Includes cumulative probability distributions, uniform probability distribution,
- Expectation and Mean

**NORMAL DISTRIBUTION **

- The Normal Distribution and Control Charts
- Graphing Calculator for Normal Distribution
- Continuous Probability Distribution Several Problems on finding the probability using the normal distribution curve. Using z scores find the probability by determining the area.
- The Standard Normal Distribution - Z-Scores and Probability, Area Underneath the Curve:
- The Z-Score
- Normal distribution: Questions, and Solutions
- Normal approximations to distributions: Questions and Solutions

**BINOMIAL DISTRIBUTIONS **

- Bernoulli Trials
- Binomial Distribution
- Binomial Distribution Four worked examples on the use of the binomial formula to calculate probability for single and cumulative binomial probability calculations. Also features a probability calculator. Examples relate to determining probabilities of exact number of successes, or greater than or less than an exact number of successes.
- Binomial Distribution Example with Formula Listing Classical binomial problem related to dice with solution.
- Binomial Distribution Approximately 10 example binomial distribution problems with explained solutions. Calculating exact probabilities. Examples for calculating mean, standard deviation and variance using binomial distribution equations.
- Binomial Distribution Problems, Percentage / Ratio Based, Solution and Explanation, Normal approximation to the binomial distribution,
- Binomial Distribution Problems Includes an introduction to the binomial distribution. Includes fairly complex examples with solutions. Illustrates the use of binomial distribution for the exactly case and the at least case.
- Binomial Distribution Problems and Solutions A very simple and easy to understand introduction to the binomial distribution. The binomial distribution is discussed and explained in context to the flipping of coins successively. The formula for the binomial distribution is given for computing the probability for a given number of success and a range of a given number of successes. The equations for the mean and standard deviation for the binomial distribution are also given.
- General Overview of Binomial Distribution from Wikipedia
- From Yale University this document about the binomial distribution is at an intermediate level. Gives generalized examples that make use of MathCad and calculator software Lists the four conditions that must be met to apply the binomial distribution.
- Solving Binomial Problems with the TI-83 Calculator. Provides two step-by-step instructions for calculating the binomial distribution with the TI-83 calculator. The exactly case is given and the case for calculating the probability for a range of successes.
- Probability distribution calculations using the TI-83.Also includes geometric distribution calculator instructions.
- Generating a binomial probability distribution for a given number of trials with the TI-83. for varying number of successes given the probability of the outcome. Uses the list function and the binompdf function without the number of successes, x, specified.
- Review of basic TI-83 Functions binompdf and normpdf functions to generate binomial distributions and to calculate the probability of a given number of successes or a given range of success.
- Probability Distribution Commands on the TI A fairly concise instructing guide on using the binomial distribution and normal distribution functions to calculate exact probability and probabilities of a range of events. One of the better ones for review Normalcdf, invnorm, binompdf and binomcdf functions are covered. .http://www.math.uic.edu/~prwesolek/math118_f09/ProbabilityCommands.pdf
- An introduction to the binomial distribution focused on using the TI-83 to calculate the problems. Fairly basic and straightforward. Includes binomial formula and an introduction to using the sequence command to generate lists of numbers.
- Binomial Distribution Probability and Cumulative Probability Distribution on the TI83 Calculator. Illustrates different ways of using the calculator for binomial distribution calculations. Shows how to sum of binomial distributions in two different ways for at most and at least cases. Provides a summary of the functions to use for exactly, at least and at most problems.
- Binomial distribution: questions, and solutions to typical binomial problems.

**POISSON DISTRIBUTION**

- Poisson Distribution. Definition of Poission distribution and notation used. Includes formula for Poision Distribution and two Poission distribution problems with solutions. One Poisson problem relates to finding a specific Poission distribution to find the probability one rate (homes in a day sold) will occur on a particular day and the cummulative probability of seeing fewer than 4 lions in a day.
- Poisson Distribution Approximation to the Binomial. Includes a detailed discussion of when to use the Poisson distribution instead of the binomial. Several problems are included with solutions. Advanced problems require the use of a frequency distribition table to determine the probability of rate-oriented events.
- General Guidelines for Determining When to use the Poisson Probability Distribution
- Poisson problems that involve the conversion of a given rate to the correct value of the gamma parameter to be used in the Poisson distribution.
- Poisson Examples With TI-83 Calculation. Several poisson problems with solutions are presented using the single value poisson TI fiunction, poissonpdf and the cummulative Poisson TI function, poissoncdf. Poisson distribution problems for exactly, at least, at most and inclusive probablities are given.
- Poisson distribution questions and solutions .

**CENTRAL LIMIT THEREOM**

- Introduction to the Central Limit Thereom. Several written pages, graphs and animations that illustrate the Central Limitation Thereom concept and its implications.
- The Law of Large Numbers and the Central Limit Thereom
- The Central Limit Theorem

**CONFIDENCE INTERVALS Z-TEST and T-TEST: Using the TI-83 Calculator **

- Calculating Confidence Intervals for the Population Mean and Poplulation Proportion Using the TI-83 Calculator: Several example problems that show you how to solve Z-Test confidence intervals with the TI-83 calculator. The calculator is used to determine the confidence interval using the Z-Test and the T-Test for the population mean and the population proportion. As well, the Z-Test and the T-Test are used to find the confidence interval for the difference between two population means and the difference between two population proportions.

**LINEAR REGRESSION**

- Linear Regression Overview. Wikipedia, Linear Regression http://en.wikipedia.org/wiki/Linear_regression
- Animated Tutorial on Lineare Regression. Givea a basic and easy to understand introduction to the concept of linear regression. http://www.roundworldmedia.com/linear/linear.html
- Linear Regression Calculator: Calculates the slope, y-intercept and the linear regression equation for a set of (x,y) coordinates. You enter the x,y coordinates in a table then press calculate to operate the online calculator. http://easycalculation.com/statistics/regression.php
- Linear Regression Calculator: Calculates and Plots the linear regression line for a set of (x,y) coordinates entered. You enter in the x,y coordinates in a text box, with the x and y values separated by commas. The calculator also lists the slope, y-intercept, the linear regression equation, the mean value of y, the mean value of x and the sample size (the number of x,y points used to produce the graph. Use the calculator also to predict a value of y from a value x after you have graphed the linear regression equation. The calculator produces a nice plot with points that are easy to distinguish.
**LINK:**Alculas: Statistisc, Linear Regression, http://www.alcula.com/calculators/statistics/linear-regression/

**PROPORTIONS Z=TEST **

- Mat 201 Practive Midterm: http://www.ltcconline.net/greenl/courses/201/keys/pmid3key.htm#1
- Proportions from two independent samples: Questions and Solutions
- Proportion from a single population questions and solutions

**T-TEST**

**MEANS**

- Mean from a single population questions and solutions
- Means from two independent samples: Questions and Solutions
- Means from paired samples: Questions and Solutions

**CONFIDENCE INTERVALS**

- Confidence Intervals
- Confidence Intervals
- Confidence Intervals: Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal

**CONFIDENCE INTERVAL FOR A MEAN**

**CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO MEANS**

- Confidence Intervals for the Difference Between Two Population Means or Proportions http://www.ltcconline.net/greenl/courses/201/Estimation/ciDifferences.htm

**CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN SEVERAL MEANS**

**CONFIDENCE INTERVAL FOR A PROPORTION**

- Confidence Intervals For Proportions and Choosing the Sample Size http://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm
- Confidence Intervals For Proportions and Choosing the Sample Size http://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm

**HYPOTHESIS TESTING **

- Hypothesis Testing
- Hypothesis Testing For a Population Mean
- Hypothesis Testing for a Proportion and for a Mean with Unknown Population Standard Deviation
- Difference Between Means Hypothesis Testing of the Between Two Means
- Hypothesis Testing - Proportions
- Hypothesis Test, Difference Between Two Means, http://www.ltcconline.net/greenl/courses/201/keys/pmid3key.htm#2
- Hypothesis Test T Test Matched Pairs. http://stattrek.com/AP-Statistics-4/Paired-Means.aspx?Tutorial=Stat

**VARIANCE TEST - POOLED F-TEST **

- http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
- General TI-83 Tests pretty good http://www.mth.pdx.edu/~fountain/TI83.PDF
- TI83 Test if Variances are Equal P-Value http://cnx.org/content/m17075/latest/
- F-Test http://www.unm.edu/~marcusj/testingassumptions.pdf
- TI-83 F-Test Instructions http://bcs.whfreeman.com/yates2e/cat_090/ch15.820.pdf
- F-Test Tables, Animations and Other Concerns, http://www.statsoft.com/textbook/distribution-tables/#f
- http://en.wikipedia.org/wiki/Student's_t-test

**PAIRED DATA AND DIFFERENCES**

**Paired Data and Differences**- Paired Differences and Differences of Proportions
- Hypothesis Testing Introduction. Gives several multiple choice questions for hypothesis testing: Questions and Solutions
- Means from a single population: Questions and Solutions
- Proportions from a single population: Questions and Solutions
- Hypothesis Testing - Multinomial proportions from a single sample Multinomial proportions from a single sample. Problems and Questions: Questions and Solutions
- Two Means using independent samples: Questions, and Solutions
- Two Means using paired samples: Questions and Solutions
- Two Proportions using independent samples: Questions and Solutions
- Practice Problems for Section 2 Above Includes 12 problems with solutions

**LINEAR REGRESSION **

- Scatter Diagrams and Regression Lines
**Correlation**Definition http://www.ltcconline.net/greenl/courses/201/regression/corr.htm- Analyzing the Regression Line
- Inferences on the Regression Line
- Trends: Questions and solutions
- Least squares: questions and solutions
- Correlation: questions and solutions

**ANOVA**

- ANOVA
- Two Way ANOVA
- Analysis of Variance
- General: Questions and Solutions
- CRD: Questions and Solutions
- RCB: Questions and Solutions
- Analysis of Variance One-Way ANOVA from Summary Data Calculator. The calculator generates a complete one-way analysis of variance (ANOVA) table for up to 8 groups. You enter the number of subjects, the mean and the standard deviation for each group in the table and the calculator generates the one-way table that provides the sum of squares, the degrees of freedom, the mean square, the fisher F-value, and the significance (p value) for between groups, within groups and total. LINK: Statistics Calculators, http://www.danielsoper.com/statcalc/calc43.aspx

**CHI-SQUARE **

There are several types of Chi Square tests. These include a Chi Square test to determine if two standard deviations are equal, if two variances are equal, the Chi Square goodness of fit test, the Chi Square goodness of fit test for normally distributed data, the Chi Square independance test, and the Chi Square homogencity of proportions test. For the goodness of fit test, a frequency distribution table is most often given and is used to determine if the frequency distribition matches a given frequency distribution or pattern, such as equally distributed preferences or if the given frequency distibution matches a normally distributed pattern (or statisical distribution). Both the Chi Square independence test and homogenicty test use contingency tables, also known as two-way tables.

The independence test is used to test whether two variables are independent. For example, to find if personal income is dependent or independant of the sex of the gender. For these types of tests, one often wants to find out if a company is discriminated against a gender through lower salaries. If discrimination is to be proved, then in this case income would be dependent on gender. If no discrimination existed, then the test would indicate that there is no relationship between pay and gender and the two variables are indendent.

The last test, the Chi Square homogencity of proportions test, is used to determine whether or not different populations have similar characterisitics. For example, with this test could be used to determine if country of Norway, Germany and the United States have statisically different arthritis or lung cancer rates. . In homogencity tests, the null hypothesis is most often that the different populations have the same population characteristics. For this example, the null hypothesis would be that Norway, Germany and the Untied States have the same arthritis rates. The alternative hypothesis would be that they have the same arthritis rate.

- Chi Square and Two Way Tables
- Chi-square tests and contingency tables
- Chi Square Test Statisitic
- Problems and Solutions Chart Based
- Problems and Solutions Texas Instrument TI-83, TI-84 and TI-89 Calculator Based Explained Solutions
- Formula and Equation Cheat Sheets
- Online Calculators

**CHI SQUARE GOODNESS OF FIT TEST **

- Goodness of Fit Chi-Square Goodness of Fit Example Problems With Solutions. This example is a casino problem related to a dice based gambling application. The problem requires that yuo determine the expected values for the roll of zero sizes, one six, two sixes, and three sixes when you roll three 6 sided dice. Using these expected values the casino manager must determine if the dice a player is using are fair dice using the Chi Square test statistics and the Chi Square goodness of fit test. Yale University, Statistics 101 http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm
- This statistics tutorial from Statek discusses the basics of the Chi-Square test statistics and the steps to use for solviong goodness of fit problems. That is the steps to determine whether or not an observed set of data matches the expected set of data. The tutorial also gives a problem with a solution. The problem is determine whether or not the claim that a toy company's cards has 30 percent rookies, 60 percent veterans and 10 percent all-stars. A random sample of cards is selected with 50 rookies, 45 veterans and 5 all stars. The problem is solved in four steps: state the hypothesis, fomulate an analysis plan, analyize sample data and interpret results. More specifically these steps includes state the null and alternative hypothesis, set the significanc level if not given, calculate the degrees of freedom, calculate the expected frequency counts and compute the chi sqaure test statistics. The next step for this solution is to compute the p-value. A chi-square statisitcs calculator in the tutorial is used to compute the p-value. .The tutorial link is Statreek: A Statistics Tutorial: Chi Square Goodness-of-Fit Test http://stattrek.com/AP-Statistics-4/Goodness-Of-Fit.aspx?Tutorial=AP. The Chi-Square statistics calculator link is Stattrek: Chi Square Distribution Calculator, Online Statistical Table http://stattrek.com/Tables/ChiSquare.aspx
- Problems and Solutions Chart Based
- Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions
- Formula and Equation Cheat Sheets
- Online Calculators

**Chi Square Test for Independence**

- Tests for independence: questions and solutions (pdf),

**Chi Square Test of Homogenity of Proportions**

**Chi Square Test for Multinominal Distributions**

- Childrens Mercy Hosptials and Clinics: Testing Multiniminal Proportions http://www.childrens-mercy.org/stats/weblog2004/MultinomialProportions.asp
- TI-83: The Chi Square Test, A Multimnominal Example with the TI-83 Calculatro
- http://www.occc.edu/statistics/StatPDF/chi%5E2.pdf
- http://biology.nebrwesleyan.edu/courses/labs/biology_of_animals/chi-square_flash.html
- http://www.cbu.edu/~wschrein/media/Stat/TI89man.pdf
- http://education.ti.com/downloads/guidebooks/graphing/83p/83m$book-eng.pdf
- http://www.tc3.edu/instruct/sbrown/ti83/gof89.htm
- http://jekyll.math.byuh.edu/courses/m221/handouts/handout22_goodness.pdf
- PowerPoint Presentation www.usm.maine.edu/~smax/course_material/lf4_10.ppt

**Chi-Square Online Calculators**

- Chi-Square Calculator, Gives an Introduction to Chi Square mathematics and mathematical formulas. . The calculator calculates the Chi-Square value after entering a given probablity and degrees of freedom http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html
- Chi Square Goodness of Fit Test Calculater: Provides an overview of the Chi-Square tests of independence and goodness-of-fit tests. The goodness of fit calculator permits you to enter data in contingency table and then automatically calculates the Chi-Square test statistic, the degrees of freedom, the p-value, the Yates Chi Square and the Yates p-value. The chi-square independence calculator requires that you enter the observed and expected values in the table. The calculator will calculate the Chi Square test statistic, the degrees of freedom and the p-value. From the p-value you can determine whether or not the data is independent or dependent. Data that is independant will no show no relationship between two variables while dependent variables will. A loaded pair of dice in a gambling game will show a dependent relationship, while a fair pair of dice won't. Dice manufacturers must make sure that the dice are manufactured such that the dice have a homogenous density throughout and are symmetrical, otherwise the dicce when rolled will produce results that are skewed towards a given number. LINK People: Calculation fr the Chi-Square Test. http://people.ku.edu/~preacher/chisq/chisq.htm
- GraphPad QuickCalcs: Compare Observed and Expected Frequencies: This calculator compares observed and expected frequencies with the Chi-Square Test. http://www.graphpad.com/quickcalcs/chisquared1.cfm

**Preparing for Your Final: Statistics Review Sheets, Cheat Sheets, Test Prep Sheets, Sample Problems**

- Formula and Equation Cheat Sheets on Basic Statistical Concepts for Measurement, Histograms, Skewed Distributions, Measures of Central Tendency, Percentile Determination. Comparing Measures of Central Tendency
- Practice Problems for Statistics Final Eight worked problems with solutions emphasizing key elementary statistics concepts and principles.
- Practice Problems for Statisitics Final Includes 8 problems with solutions
- GMAT Probability Problems. Over 100 pages of solved probability problems for the GMAT. Problems use permutations, counting theory and logic to determine the answers.

**TI-83 / TI-84 / TI-89 STATISTICS CALCULATOR REFERENCES**

- TI-83 and TI-84 Calculator Statistics Reference Book, Chapter 12. A complete manual, over 690 pages, on the use of the TI-84 calculator, Chapter 12 and Chapter 13 are dedicated to statistics problems using the TI-84 calculator.
- TI-83 Statistics Command Summary. Includes 11 pages of TI-83 commands used in statistics with links to examples.
- TI-83 Example Problems and Solutions using the TI-83 for common elementary statistics problems. Includes a complete summary of problems for binomial, normal, poisson, Student t, Chi-Square, and F Distributions. Also provides examples on how to use TI-83 to solve hypothesis problems and regression problems Also provides details on how to make distribution plots on the TI-83's screen
- Stepped Instructions Using the TI-83 Calculator for Solving Common Elementary Statistics Problems. Provides concise steps for using the TI-Calculator to solve confidence interval, distribution, hypothesis and regression problems Details steps for graphing also.

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PROBABIITY

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**CONDITIONAL PROBABILITY**

Problems and Solutions Chart Based

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**INDEPENDENCE**

Problems and Solutions Chart Based

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**NORMAL DISTRIBTION**

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**Z-SCORE AND NORMAL DISTRIBUTION**

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**Z-SCORE AND THE MEAN **

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**CENTRAL LIMIT THEREOM**

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**Z-SCORE AND PROPORTIONS**

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**Z-SCORE AND DIFFERENCE BETWEEN TWO MEANS**

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**Z-SCORE AND DIFFERENCE BETWEEN TWO PORPORTIONS**

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**T-SCORE AND NORMAL DISTRIBUTION**

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**T-SCORE AND THE MEAN **

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**T-SCORE AND PROPORTIONS**

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**T-SCORE AND DIFFERENCE BETWEEN TWO MEANS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND DIFFERENCE BETWEEN TWO PROPORTION**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**HYPOTHESIS TESTING **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**REGRESSION **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**ANOVA **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**BASIC STATISTCS **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

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Online Calculators

PROBABIITY

Problems and Solutions Chart Based

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Online Calculators

**CONDITIONAL PROBABILITY**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

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Online Calculators

**INDEPENDENCE**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**NORMAL DISTRIBTION**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**Z-SCORE AND NORMAL DISTRIBUTION**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**Z-SCORE AND THE MEAN **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**CENTRAL LIMIT THEREOM**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**Z-SCORE AND PROPORTIONS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**Z-SCORE AND DIFFERENCE BETWEEN TWO MEANS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**Z-SCORE AND DIFFERENCE BETWEEN TWO PORPORTIONS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND NORMAL DISTRIBUTION**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND THE MEAN **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND PROPORTIONS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND DIFFERENCE BETWEEN TWO MEANS**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**T-SCORE AND DIFFERENCE BETWEEN TWO PROPORTION**

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**HYPOTHESIS TESTING **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

Formula and Equation Cheat Sheets

Online Calculators

**REGRESSION **

Problems and Solutions Chart Based

Problems and Solutions Texas Instrument TI-83 and TI-84 Calculator Based Explained Solutions

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Online Calculators

**GOODNESS OF FIT **

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**CHI-SQUARE **

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Online Calculators

**ANOVA **

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Online Calculators

Statistics Introduction

Measures of Central Tendency

Descriptive Statistics

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Description: Hundreds of statistics problems with solutions for learning college level elementary statistics. Complete with personalized tutoring services, contact mark.c.stansberry@gmail.com for Santa Rosa Junior College and Sonoma State University statistics tutoring.

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