20804240Basic Statistics
Course Information
Description
Appropriate statistical techniques are studied for the systematic collection, presentation, analysis and interpretation of experimental results, including surveys and quality control. The focus is on understanding the techniques of statistical inference (confidence intervals and hypothesis testing) and interpreting results as found in articles and reports. Emphasizes the inherent uncertainty when decisions are made based on sample data. Includes descriptive statistics, basic probability theory, sampling distributions and the Central Limit Theorem; the binomial, normal, Student t, chi-square, and F distributions; and techniques of 1- and 2-sample tests, linear regression, correlation, and an introduction to analysis of variance. 
Total Credits
4
Prior Learning Assessment
  • Exam-College Developed Challenge Exam
Course Competencies
  1. Analyze the importance of statistics in modern life
    Assessment Strategies
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    Criteria
    identify concrete situations in a variety of disciplines and in ordinary life where the knowledge of statistics is essential
    analyze the importance of statistics advancing science and acquiring knowledge

  2. Employ appropriate language in describing research data
    Assessment Strategies
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    Criteria
    distinguish between population and sample data
    differentiate data as quantitative or qualitative
    identify numerical data as measuring at the nominal, ordinal, interval or ratio level
    explain the importance of random sampling for making statistical inference
    compare different random sampling techniques identifying situations for which each is appropriate
    determine whether a study is observational or experimental and recognize different methods appropriate to each
    assess a given study as to the presence and likely importance of confounding variables

  3. Employ appropriate representations of sample data
    Assessment Strategies
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    Criteria
    generate frequency distributions from a given set of sample data
    construct a histogram to represent a distribution
    construct scatter plot diagram of bivariate data
    identify the most appropriate form for representing a distribution given the type of data and the questions being asked

  4. Calculate measures of central tendency
    Assessment Strategies
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    Criteria
    calculate the mean of a data set
    calculate the median of a data set
    calculate the mode of a data set
    recognize variations in procedures for computing each of the measure given for specific circumstances
    evaluate the appropriateness of each measure of central tendency given the type of data and research concerns

  5. Calculate measures of spread
    Assessment Strategies
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    Criteria
    calculate the quartile, decile and percentile ranks for a given data set
    interpret the quartile, decile and percentile ranks as measures of position
    calculate the range for a given data set
    calculate the population or sample standard deviation for a given set of data
    calculate the interquartile range for a given data set
    evaluate the appropriateness of the standard deviation, range and interquartile range as measures of spread given the type of data and research concerns

  6. Compare and contrast distributions
    Assessment Strategies
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    Criteria
    compare two distributions with respect to central tendency
    compare two distributions with respect to spread
    calculate normal scores (z-scores) for given data values
    interpret normal scores appropriately
    construct modified box-and-whiskers plots to aid comparisons
    interpret differences in center and spread of distributions in practical terms
    apply Chebyshev's theorem and the Empirical Rule to discuss limitations on variation and the meaning of 'unusual' as it applies to data values in a distribution

  7. Assess relationship between variables in a bivariate data set
    Assessment Strategies
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    Criteria
    distinguish between dependent and independent variables
    calculate the correlation coefficient
    interpret correlation coefficient appropriately
    calculate constant and slope coefficient for linear regression line using the Ordinary Least Squares procedure
    use constant and slope coefficient to graph the 'best fitting' line to a set of sample data
    make reasonable predictions using the mean of the dependent variable or the least squares prediction equation, as appropriate
    assess the strength of the linear relationship between the variables in the sample

  8. Employ general rules to compute probabilities of individual and joint probability events
    Assessment Strategies
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    Criteria
    identify probability experiments, their outcomes and random variables
    interpret probability by means of the classic, relative frequency and subjective understandings
    distinguish theoretical and empirical probabilities
    use combinatorics to compute number of outcomes in a given event
    represent sample space by listing all outcomes, using Venn diagrams, constructing tree diagrams or building tables
    use representation of the sample space and the basic definition of probability to compute probabilities of given events
    employ special and general rules of addition to compute probabilities of disjoint events
    recognize conditional probabilities
    use special and general rules of multiplication to compute probabilities of conjoint events
    distinguish between statistically dependent and independent events
    apply mathematical rules for computing probabilities to solve application problems

  9. Assess probabilities of events using probability distributions for discrete random variables
    Assessment Strategies
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    Criteria
    generate a probability distribution for a discrete random variable from empirical data
    generate a binomial distribution for appropriate random variables using formulae and tables
    calculate the mean of a given discrete distribution
    calculate the standard deviation and variance of a given discrete distribution
    compute expected values for a discrete random variable
    interpret expected value
    calculate probabilities of events based on the distribution of discrete random variables to solve application problems

  10. Assess probabilities of events using probability distributions for continuous random variables
    Assessment Strategies
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    Criteria
    employ appropriate notation and accurate sketches when representing continuously distributed random variables
    calculate probabilities of events based on a uniform distribution for a continuous random variable given appropriate parameter values
    calculate probabilities of events based on a normal distribution for a continuous random variable given appropriate parameters
    calculate probabilities of events based on the distribution of continuous random variables to solve application problems

  11. Derive distributions for sample statistics
    Assessment Strategies
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    Criteria
    apply the central limit theorem to find the mean and variance of the sample average for a given distribution
    apply the central limit theorem to determine when the distribution of a sample average follows a normal or a student's-t distribution
    calculate the mean and variance of a sample proportion by applying the binomial distribution
    determine the normality of the distribution of sample proportions
    apply the chi-square distribution to describe the distribution of sample variances

  12. Estimate population parameters using sample data
    Assessment Strategies
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    Criteria
    construct confidence interval for the population mean given sample data selecting the appropriate procedure
    construct confidence interval for the population standard deviation given sample data
    construct confidence interval for a population proportion given sample data
    interpret confidence intervals appropriately
    calculate the minimum sample size necessary to estimate a population parameter to a given level of confidence

  13. Estimate differences in population parameters using sample data
    Assessment Strategies
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    Criteria
    construct confidence intervals for differences in population means given sample data selecting the appropriate procedure
    construct confidence intervals for differences in population proportions given sample data
    interpret confidence intervals appropriately

  14. Assess the validity of statements about population parameters using sample data
    Assessment Strategies
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    Criteria
    carry out hypothesis test for the population mean given sample data using appropriate parametric procedures
    carry out hypothesis test for the population standard deviation given sample data
    carry out hypothesis test for a population proportion given sample data
    interpret hypothesis tests, drawing reasonable conclusions and stating them succinctly in standard English

  15. Assess the validity of statements about differences in population parameters using sample data
    Assessment Strategies
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    Criteria
    carry out hypothesis tests for differences in population means given sample data using appropriate parametric procedures
    carry out hypothesis tests for differences in population proportions given sample data
    interpret hypothesis tests, drawing reasonable conclusions and expressing them succinctly in standard English

  16. Assess the relationship between two variables in a population using bivariate sample data
    Assessment Strategies
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    Criteria
    compute the correlation coefficient for a set of bivariate data
    conduct a significance test on the sample correlation coefficient
    compute the constant and slope coefficients of a linear regression using the method of Ordinary Least Squares given sample data
    apply constant and slope coefficients from a linear regression to describe the relationship between variables in a bivariate sample
    construct confidence interval to estimate the expected value of the dependent variable in the population given sample data and a value of the independent variable
    construct a prediction interval to estimate the realized value of the dependent variable in the population given sample data and a value of the independent variable

  17. Assess the 'goodness of fit' of a theoretical model
    Assessment Strategies
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    Criteria
    apply an appropriate 'chi-square' procedure to assess how well a given theoretical model fits a set of sample data
    interpret hypothesis tests, drawing reasonable conclusions, and expressing them succinctly in standard English

  18. Test the independence of two categorical variables
    Assessment Strategies
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    Criteria
    perform an appropriate 'chi-square' procedure to test the independence of two categorical variables
    interpret hypothesis tests, drawing reasonable conclusions and expressing them succinctly in standard English

  19. Test the equality of sample means in a procedure involving three or more treatments
    Assessment Strategies
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    Criteria
    perform an appropriate ANOVA procedure to test the equality of means from three or more 'treatment' groups
    evaluate sample data to determine which procedure is appropriate
    interpret tests, drawing reasonable conclusions and expressing them succinctly in standard English