Unit | Unit Title | Subunit Title | Objectives |
1 | Statistics and Data | - The Science of Statistics and Its Importance
- Methods for Describing Data
| - Apply various types of sampling methods to data collection;
- Create and interpret frequency tables;
- display data graphically and interpret the following types of graphs: stem plots, histograms, and boxplots;
- identify, describe, and calculate the following measures of the location of data: quartiles and percentiles;
- identify, describe, and calculate the measures of the center of mean, median, and mode; and
- Identify, describe, and calculate the following measures of the spread of data: variance, standard deviation, and range.
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2 | Elements of Probability and Random Variables | - Classical Probability Model
- Random Variables
| - Understand and use the terminology of probability;
- Determine whether two events are mutually exclusive and whether two events are independent;
- Calculate probabilities using the addition Rules and multiplication rules;
- Construct and interpret Venn diagrams;
- Apply useful counting rules in the context of combinational probability;
- Identify and use common discrete probability distribution functions;
- Calculate and interpret expected values;
- Identify the binomial probability distribution, and apply it appropriately;
- Identify the Poisson probability distribution, and apply it appropriately.
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3 | Normal Distributions and Sampling Distributions | - Normal Distributions
- The Concept of Sampling Distributions
- Sampling Distributions for Common Statistics
| - Identify and use continuous probability density functions;
- Identify the normal probability distribution, and apply it appropriately;
- Apply the central theorem to approximate sampling distributions;
- Describe the role of sampling distributions in inferential statistics;
- Interpret and create graphs of a probability distribution for the mean and a discrete variable;
- Describe a sampling distribution in terms of repeated sampling;
- Compute the mean and standard deviation of the sampling distribution of the population;
- Identify or approximate a sampling distribution based on the properties of the population;
- Compare and evaluate the sampling distributions of different sample sizes; and
- Compare and evaluate the performance of different estimators based on their sampling distributions.
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4 | Estimation with Confidence Intervals | - Point Estimators and Their Characteristics
- Confidence Intervals
| - Explain the central limit theorem, and use it to construct confidence intervals;
- Compare t-distribution and normal distribution;
- Apply and interpret the central limit theorem for sample averages;
- Calculate and interpret confidence intervals for population averages and one population proportions; and
- Interpret the student-t probability distribution as the sample size changes.
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5 | Hypothesis Test | - Elements of Hypothesis Testing
- Tests of Population Means
| - Differentiate between type I and type II errors;
- Describe hypothesis testing in general and in practice;
- Interpret and explain how to conduct hypothesis tests for a single population mean and population proportion, when the population standard deviation is unknown;
- Interpret and explain how to conduct hypothesis tests for a single population proportion; and
- Classify hypothesis tests by type.
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6 | Linear Regression | - The Regression Model
- Fitting the Model
| - Discuss basic ideas of linear regression and correlation;
- Identify the assumptions that inferential statistics in regression are based on;
- Compute the standard error of a slope;
- Test a slope for significance;
- Construct a confidence interval on a slope; and
- Calculate and interpret the correlation coefficient.
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7 | Review | | |