Maricopa Community Colleges  MAT206   20044-20062 
Official Course Description: MCCCD Approval: 12/09/03
MAT206 20044-20062 LEC 3 Credit(s) 3 Period(s)
Elements of Statistics
Basic concepts and applications of statistics, including data description, estimation and hypothesis tests. Prerequisites: Grade of "C" or better in MAT150 or MAT151 or MAT152 or equivalent or satisfactory score on District placement exam.
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MCCCD Official Course Competencies:
 
MAT206   20044-20062 Elements of Statistics
1. Identify the difference between descriptive and inferential statistics. (I)
2. Distinguish between a population and a sample. (II)
3. Group a set of data and present the grouping in graphical form. (II)
4. Determine the mean, median, mode and standard deviation of data set and find the z-score for a data piece. (III)
5. Define random variable and the probability distribution of a random variable. (IV)
6. Find probabilities for normal random variables by using the standard normal distribution. (V)
7. Construct random samples. (VI)
8. Graph the sampling distribution of the mean for all sample sizes and all populations. (VI)
9. Find point and interval estimates of population means. (VII)
10. Describe the logic of hypothesis testing emphasizing the role of probability distributions and types of error. (VIII)
11. Perform inferences about one mean in the case of normal populations or large sample size. (VIII)
12. Perform inferences about two means in the case of normal populations or large sample size. (IX)
13. Use the Chi-square goodness-of-fit test to determine if two populations have the same shape. (X)
14. Use the Chi-square independence test to determine whether two characteristics of a population are associated (dependent). (X)
15. Identify the best-fitting regression line for a set of data points. (XI)
16. Partition the total sum of squares for a set of data points to find measures of regression line fit and linear relationship. (XI)
17. Use one-way analysis of variance to partition the total sum of squares in order to test for a difference among means. (XII)
18. Identify the difference between parametric and nonparametric statistics. (XIII)
19. Demonstrate proper use of nonparametric procedures . (XIII)
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MCCCD Official Course Outline:
 
MAT206   20044-20062 Elements of Statistics
    I. Nature of Statistics
        A. Two kinds of statistics
        B. Classification of Statistical Studies
        C. Development of Inferential Statistics
      II. Organizing Data
          A. Types of Data
          B. Grouping Data
          C. Stem-and-leaf Diagrams
          D. Misleading Graphs
        III. Descriptive Measures
            A. Measures of Central Tendency
            B. Summation Notation: the Sample Mean
            C. Measures of Dispersion: the Sample Standard Deviation
            D. Interpretation of the Standard Deviation: z-scores
            E. Percentiles: box-and-whisker Diagrams
          IV. Probability Concepts
              A. Introduction: Classical Probability
              B. Discrete Random Variables: Probability Distributions
            V. Normal Distribution
                A. Standard Normal Curve
                B. Normal Curves
                C. Normally Distributed Populations
                D. Normally Distributed Random Variables
              VI. Sampling Distribution of the Mean
                  A. Sampling: Random Samples
                  B. Sampling Error: the Need for Sampling Distributions
                  C. The Mean and Standard Deviation of the Sample Mean
                  D. The Sampling Distribution of the Mean
                VII. Confidence Intervals for One Mean
                    A. Estimating a Population Mean
                    B. Large-sample Confidence Intervals for a Population Mean
                    C. Sample Size Considerations
                    D. Confidence Intervals for a Normal Population Mean
                  VIII. Hypothesis Tests for One Mean
                      A. The Nature of Hypothesis Testing
                      B. Terms, Errors, and Hypotheses
                      C. Large Sample Hypothesis Tests for a Population Mean
                      D. Hypothesis Tests for a Normal Population
                    IX. Inferences for Two Means
                        A. Large Sample Inferences for Two Populations Means using Independent Samples
                        B. Inferences for the Means of Two Normal Populations with Equal Standard Deviations Using Independent Samples
                        C. Inferences for Two Population Means Using Paired Samples
                        D. Procedures
                      X. Chi-square Procedures
                          A. The Chi-square Distribution
                          B. Chi-square goodness-of-fit test
                          C. Chi-square Independence Test
                        XI. Methods in Linear Regression
                            A. Linear Equations with One Dependent Variable
                            B. Regression Equation
                            C. Coefficient of Determination
                            D. Linear Correlation
                            E. Inferences in Correlation
                          XII. Analysis of Variance
                              A. The F-Distribution
                              B. One-way Analysis of Variance
                            XIII. Nonparametric Statistics
                                A. Definition
                                B. Wilcoxon Signed-rank Test
                                C. The Mann-Whitney Test
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