STANDARD COMPETENCIES:

 

 1.   Recognize and give examples of statistics terms and concepts including: descriptive and inferential statistics, qualitative and quantitative data, discrete and continuous random variables, different levels of measurement, populations and samples, parameters and sample statistics.

 2.   Present and interpret various methods of depicting data including histograms, stem and leaf diagrams, box and whisker plots, line graphs, bar graphs, pie charts.

 3.   Recognize and identify various shapes of data distributions.

 4.   Present various statistical measures using proper notation including measures of central tendency (mean, median, mode, and midrange), measures of dispersion (range, variance, and standard deviation), and measures of position (z-score, percentile, quartile, and decile).

 5.   Organize data into a grouped frequency table.

 6.   Utilize the basic definitions to calculate simple probabilities.

 7.   Utilize the addition rule to calculate probabilities for the occurrence of one event or another event.

 8.   Demonstrate an understanding of how events are complementary and calculate the probability that an event does not occur.

 9.   Use counting principles to determine the number of ways various events can occur.

 10. Develop the concepts of probability distributions including the binomial.

 11. Use formulas to calculate the mean, variance, standard deviation, and expected value of a probability distribution including the binomial.

 12. Recognize and identify various shapes of probability distributions.

 13. Describe the normal distribution and the associated statistics and probabilities including area under a probability curve.

 14. Determine probabilities using the standard normal distribution.

 15. Determine scores that correspond to given probabilities.

 16. Use the normal distribution to approximate probabilities associated with a binomial experiment and know the conditions for which these approximations are appropriate.

 17. Explain the meaning of a sampling distribution and apply the central limit theorem.

 18. Develop point estimates and interval estimates (confidence intervals) for population means, proportions, and variance (including chi squared).  Determine sample size for a population mean and population proportion.

 19. Perform a hypothesis test on one mean and other parameters.

 20. Calculate and interpret the correlation coefficient.  Find a line of best fit applying the concept of residuals.

 

 TOPICAL OUTLINE:

 

 I.      Introduction

         A.      Branches of Statistics

         B.      Types of Data & Levels of Measurement

         C.      Population of Bivariate Data

 II.     Data Presentation and Summarization

         A.      Exploratory Data Analysis

         B.      Histograms, Stem and Leaf Diagrams, Box Plots

         C.      Measures of Central Tendency and Dispersion

         D.      Presentation of Bivariate Data

 III.    Probability

         A.      Fundamentals

         B.      Addition Rule

         C.      Multiplication Rule

         D.      Complimentary Events

         E.      Counting

 IV.     Probability Distributions

         A.      Random Variables

         B.      Mean, Variance, Expectation

         C.      Binomial Distributions

         D.      Distribution Shapes

 V.      Normal Distributions

         A.      Standard

         B.      Nonstandard

         C.      Normal as Approximate of Binomial

         D.      The Central Limit Theorem

 VI.     Estimates and Sample Sizes

         A.      Circles

         B.      Confidence Intervals for Means

         C.      Confidence Intervals for Proportions

         D.      Confidence Intervals for Variances

         E.      Chi Square & Goodness of Fit

 VII.    Testing Hypothesis

         A.      Tests & Involving One Mean

         B.      Tests of Other Parameters

 VIII.   Correlation and Regression

         A.      Correlation

         B.      Regression

         C.      Analysis of Residuals