## MCR 5 - Learning Support for Statistical Reasoning at Northern Virginia Community College

### Course Description

Effective: 2017-08-01

Provides instruction for students who require minimum preparation for college-level Statistical Reasoning. Students in this course will be co-enrolled in MTH 155. Credits not applicable toward graduation and do not replace MTE courses waived. Successful completion of Statistical Reasoning results in the prerequisite MTE modules being satisfied.

Lecture 1-2 hours. Total 1-2 hours per week.

1-2 credits

### General Course Purpose

To enable qualified students to enter into credit bearing courses sooner, with the appropriate support, and with equal or better success than those students meeting course prerequisite requirements. The course provides support and enhancement of foundational and course content required of the credit course.

### Course Prerequisites/Corequisites

Prerequisites: Completion of any three of the MTE modules 1-5 and Corequisite: MTH 155: Statistical Reasoning

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Use appropriate statistical language in oral, written, and graphical terms.
- Read and interpret graphs and descriptive statistics.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Understand what statistical question is being addressed, use appropriate strategies to answer the question of interest, and state conclusions using appropriate statistical language.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
- Support conclusions by providing appropriate statistical justifications.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Identify errors such as inappropriate sampling methods, sources of bias, and potentially confounding variables, in both observational and experimental studies.
- Identify mathematical or statistical errors, inconsistencies, or missing information in arguments.
- Technology
- Use appropriate technology in a given context.
- Use some form of spreadsheet application to organize information and make repeated calculations using simple formulas and statistical functions.
- Use technology to calculate descriptive statistics and test hypotheses.
- Graphical and Numerical Data Analysis
- Identify the difference between quantitative and qualitative data
- Identify the difference between discrete and continuous quantitative data
- Construct and interpret graphical displays of data, including (but not limited to) box plots, line charts, histograms, and bar charts
- Construct and interpret frequency tables
- Compute measures of center (mean, median, mode), measures of variation, (range, interquartile range, standard deviation), and measures of position (percentiles, quartiles, standard scores)
- Sampling and Experimental Design
- Recognize a representative sample and describe its importance
- Identify methods of sampling
- Explain the differences between observational studies and experiments
- Recognize and explain the key concepts in experiments, including the selection of treatment and control groups, the placebo effect, and blinding
- Probability Concepts
- Describe the difference between relative frequency and theoretical probabilities and use each method to calculate probabilities of events
- Calculate probabilities of composite events using the complement rule, the addition rule, and the multiplication rule
- Use the normal distribution to calculate probabilities
- Identify when the use of the normal distribution is appropriate
- Recognize or restate the Central Limit Theorem and use it as appropriate
- Statistical Inference
- Explain the difference between point and interval estimates
- Construct and interpret confidence intervals for population means and proportions
- Interpret the confidence level associated with an interval estimate
- Conduct hypothesis tests for population means and proportions
- Interpret the meaning of both rejecting and failing to reject the null hypothesis
- Use a p-value to reach a conclusion in a hypothesis test
- Identify the difference between practical significance and statistical significance
- Correlation and Regression
- Analyze scatterplots for patterns, linearity, and influential points
- Determine the equation of a least-squares regression line and interpret its slope and intercept
- Calculate and interpret the correlation coefficient and the coefficient of determination
- Categorical Data Analysis
- Conduct a chi-squared test for independence between rows and columns of a two-way contingency table
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation:
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Domain and Range
- Graphing linear equations and inequalities
- Writing equations of lines given specific information
- Solving first degree equations and inequalities
- Evaluating expressions/functions for given values of variables
- Manipulating equations to solve for a given variable.
- Excel or similar applications
- Formulas
- Ratios and Proportions

### Major Topics to be Included

- Graphical and Numerical Data Analysis
- Sampling and Experimental Design
- Probability
- Statistical Inference
- Correlation and Regression