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MATH 115 - Introduction to Statistical Methods

Number of Credits: 4
Develop essential skills and knowledge required for proficient statistical analysis and inference. Communicate statistical concepts using precise symbols, notation, and vocabulary through a combination of theory and practical application. Explore data summarization, probability computation, hypothesis testing, and the utilization of technology for accurate statistical problem-solving. Advanced Placement Exam-'Statistics with a score of 3' accepted.  (Fall, Spring & Summer Only) Four hours lecture each week. Four Credits. Four billable hours.

GENERAL EDUCATION. Category: Mathematics

Pre-requisite(s): eligibility for ENGL 101 , plus exemption from or completion of MAT 094 , MAT 095 , or MAT 099   with a minimum grade of C, a satisfactory MATH placement measure, or any college level MATH course. 
Course Topics:
 

  1. Introduction to Statistical Concepts:
    • Notation, symbols, and terminology in statistics
    • Types of data and measurement scales
  2. Data Summarization and Visualization:
    • Measures of central tendency (mean, median, mode)
    • Measures of variability (range, variance, standard deviation)
    • Data visualization techniques (histograms, box plots, scatter plots)
  3. Probability:
    • Probability distributions (Binomial, Normal)
    • Probability calculations for discrete and continuous random variables
  4. Central Limit Theorem:
    • Understanding and applying the Central Limit Theorem
    • Sampling distribution of the sample mean
  5. Confidence Intervals:
    • Construction and interpretation of confidence intervals
    • Confidence intervals for population means and proportions
    • Confidence intervals for differences between means and proportions
    • Confidence intervals for linear correlations
  6. Hypothesis Testing:
    • Hypothesis testing fundamentals
    • One-sample and two-sample hypothesis tests
    • Tests for population means and proportions
    • Tests for linear correlations
  7. Chi-Squared Tests:
    • Chi-squared test for independence
    • Chi-squared goodness-of-fit test
  8. Technology in Statistical Analysis:
    • Utilizing statistical software

Course Objectives: Upon successful completion of this course, students will be able to:
 

  1. Articulate statistical concepts using appropriate symbols, notation, and vocabulary, ensuring accurate and clear communication of ideas and results. (GE1)
  2. Summarize data using a variety of methods. (GE2, GE5)
  3. Identify probabilities for both discrete and continuous random variables. (GE2, GE3, GE5)
  4. Interpret the Central Limit Theorem when dealing with sample means, allowing for robust statistical inference. (GE1, GE2, GE3, GE5)
  5. Construct confidence intervals using sample data to estimate population parameters and linear correlations. (GE1, GE2, GE3, GE5)
  6. Conduct hypothesis tests to make informed inferences about population parameters and linear correlations based on sample data, providing a solid foundation for decision-making. (GE1, GE2, GE3, GE5)
  7. Employ chi-squared distributions for hypothesis testing and analysis in various statistical scenarios. (GE1, GE2, GE3, GE5)
  8. Utilize modern technology and statistical software tools effectively to accurately solve complex statistical problems and enhance decision-making. (GE5)


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