Revised 08/2024

MDE 55 - Learning Support for Statistical Reasoning (3 CR.)

Course Description

Provides support to ensure success for students co-enrolled in Statistical Reasoning (MTH 155). Course will review foundational topics through direct instruction, guided practice, and individualized support. Lecture 3 credits. Total 3 hours per week.

General Course Purpose

This course provides support to ensure student success with the MTH 155 objectives.

Course Prerequisites/Corequisites

Corequisite: MTH 155

Course Objectives

Upon completing the course, the student will be able to:

• 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.
    • Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
• 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
  • o 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.

Major Topics to Be Included

• Arithmetic and order of operations
• Operations with fractions, percentages, and decimals
• Exponents
• Formulas
• Units and measurement
• Simplifying algebraic expressions and solving linear equations
• Using technology including calculators and spreadsheet software