蘑菇短视频

Skip to main content

MATH 270 Syllabus

Statistical Methods I

Revised: January 6, 2020

Course Description

Descriptive statistics, correlation, least square regression, basic probability models, probability distributions, central limit theorem, confidence intervals, hypothesis testing.
Prerequisite: MATH 146 or 153 or placement.
Three semester hours.

Student Learning Objectives

  1. Describe the concepts of population and sample, and some of the basic descriptive measures associated with them.
  2. Explain graphical methods for data presentation.
  3. Connect the concepts of probability, random variables, and distributions.
  4. Assess the properties of common distributions, especially the normal and binomial.
  5. Synthesize the ideas of correlation and regression.
  6. Interpret estimation and hypothesis testing procedures applied to population means and proportions.
  7. Compare multiple means and proportions using appropriate statistical analyses.
  8. Model univariate and multivariate data using linear models.

Text

Roxy Peck, Chris Olsen, and Jay DeVore. Introduction to Statistics and Data Analysis, Fourth Edition. (Brooks-Cole/Cengage Learning), 2011.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

Chapters 1-5 can be covered as necessary.

  • Chapter 1: The Role Of Statistics.
  • Chapter 2: The Data Analysis Process And Collecting Data Sensibly.
  • Chapter 3: Graphical Methods For Describing Data.
  • Chapter 4: Numerical Methods For Describing Data.
  • Chapter 5: Summarizing Bivariate Data.
  • Chapter 6: Probability. (1.5 weeks)
    Chance Experiments and Events. Definition of Probability. Basic Properties of Probability. Conditional Probability. Independence.
    Note: Sections 6.6 and 6.7 are optional.
  • Chapter 7: Random Variables and Probability Distributions. (1 week)
    Random Variables. Probability Distributions for Discrete Random Variables. Probability Distributions for Continuous Random Variables. Mean and Standard Deviation of a Random Variable. The Binomial Distribution. Normal Distributions.
    Note: The topic of Geometric Distributions in Section 7.5, and Sections 7.7. 7.8 are optional.
  • Chapter 8: Sampling Variability And Sampling Distributions. (1 week)
    Statistics and Sampling Variability. The Sampling Distribution of a Sample Mean. The Sampling Distribution of a Sample Proportion. Note: Consider having Exam 2 after Chapter 8.
  • Chapter 9: Estimation Using A Single Sample. (1 week)
    Point Estimation. A Large Sample Confidence Interval for a Population Proportion. A Confidence Interval for a Population Mean. Communicating and Interpreting the Results of Statistical Analyses.
  • Chapter 10: Hypothesis Testing Using A Single Sample. (2 weeks)
    Hypotheses and Test Procedures. Errors in Hypothesis Testing. Large-Sample Hypothesis Tests for a Population Proportion. Hypothesis Tests for a Population Mean. Note: Section 10.5 is optional.
  • Chapter 11: Comparing Two Populations or Treatments. (1 week)
    Inferences Concerning the Difference Between Two Populations or Treatment Means Using Independent Samples. Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples. Large-Sample Inferences Concerning the Difference Between Two Populations or Treatment Proportions. Interpreting the Results of Statistical Analyses.
  • Chapter 12 The Analysis Of Categorical Data And Goodness-Of-Fit Tests. (1 week)
    Chi-square Tests for Univariate Data. Tests for Homogeneity and Independence in a Two-way Table. Interpreting the Results of Statistical Analyses.
  • Chapter 13: Simple Linear Regression and Correlation: Inferential Methods. (1 week)
    Simple Linear Regression Model. Inferences About the Slope of the Population Regression Line. Checking Model Adequacy. Inferences Based on the Estimated Regression Line (Optional). Inferences About the Population Correlation Coefficient (Optional). Interpreting the Results of Statistical Analyses.
  • Chapter 14: Multiple Regression Analysis. (1 week)
    Multiple Regression Models. Fitting a Model and Assessing Its Utility. Inferences Based on an Estimated Model. Other Issues in Multiple Regression. Interpreting and Communicating the Results of Statistical Analyses.
  • Chapter 15: Analysis of Variance. (0.5 week)
    Single-Factor ANOVA and the $F$ Test. Multiple Comparisons. The $F$ Test for a Randomized Block Experiment. Two-Factor ANOVA. Interpreting the Results of Statistical Analyses.

* Note: Most instructors for this course require the use of statistical calculators.