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Analyze the importance of statistics in modern life
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Employ appropriate language in describing research data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Employ appropriate representations of sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Calculate measures of central tendency
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Calculate measures of spread
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Compare and contrast distributions
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess relationship between variables in a bivariate data set
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Employ general rules to compute probabilities of individual and joint probability events
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess probabilities of events using probability distributions for discrete random variables
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess probabilities of events using probability distributions for continuous random variables
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Derive distributions for sample statistics
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Estimate population parameters using sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Estimate differences in population parameters using sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess the validity of statements about population parameters using sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess the validity of statements about differences in population parameters using sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess the relationship between two variables in a population using bivariate sample data
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Assess the 'goodness of fit' of a theoretical model
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Test the independence of two categorical variables
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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
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Test the equality of sample means in a procedure involving three or more treatments
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
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