# MATH 270 Syllabus

### Statistical Methods I

Revised: September, January 2015

## Course Description

Descriptive statistics, correlation, least squares regression, basic probability models, probability distributions, central limit theorem, conﬁdence intervals, hypothesis testing. Prerequisite: MATH 140 or above. Three semester hours.

## Objectives

By the end of the course students will be able to

• Describe the concepts of population and sample, and some of the basic descriptive measures associated with them;
• Explain graphical methods for data presentation;
• Connect the concepts of probability, random variables, and distributions;
• Assess the properties of common distributions, especially the normal and binomial;
• Synthesize the ideas of correlation and regression;
• Interpret estimation and hypothesis testing procedures applied to population means and proportions;
• Compare multiple means and proportions using appropriate statistical analyses; and
• 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 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

• Chapter 1: The Role Of Statistics. (1 day)
Why Study Statistics? The Nature and Role of Variability. Statistics and the Data Analysis Process. Types of Data and Some Simple Graphical Displays

• Chapter 2: The Data Analysis Process And Collecting Data Sensibly. (4 days)
Statistical Studies: Observation and Experimentation. Sampling. Simple Comparative Experiments. More on Experimental Design. Interpreting and Communicating the Results of Statistical Analyses.
Note: Section 2.5 is optional.

• Chapter 3: Graphical Methods For Describing Data. (4 days)
Displaying Categorical Data: Frequency Distributions, Bar Charts and Pie Charts. Displaying Numerical Data: Dotplots and Stem-and-Leaf Displays. Displaying Numerical Data: Frequency Distributions and Histograms. Interpreting the Results of Statistical Analyses. Note: Section 3.1 is optional and Section 3.4 may be taught concurrently with Section 5.1. The topic of density histograms in Section 3.3 is optional.

• Chapter 4: Numerical Methods For Describing Data. (3 days)
Describing the Center of a Data Set. Describing Variability in a Data Set. Summarizing a Data Set: Boxplots. Interpreting Center and Spread: Chebyshev's Rule, The Empirical Rule, and z-Scores. Interpreting the Results of Statistical Analyses. Note: The topic of trimmed means in Section 4.1 is optional.

• Chapter 5: Summarizing Bivariate Data. (2 days)
Scatter Plots. Correlation. Fitting a Line to Bivariate Data. Assessing the Fit of a Line. Nonlinear Relationships and Transformations. Interpreting the Results of Statistical Analyses. First steps, design of experiments, sampling design, toward statistical inference. Note: Sections 5.4 and 5.5 are optional.

• Chapter 6: Probability. (3 days)
Interpreting Probabilities and Basic Probability Rules. Probability as a Basis for Making Decisions. Estimating Probabilities.

• Chapter 7: Population Distributions. (4 days)
Describing the Distribution of Values in a Population. Population Models for Continuous Numerical Variables. Normal Distributions. Checking for Normality and Normalizing Transformations.

• Chapter 8: Sampling Variability And Sampling Distributions. (3 days)
Statistics and Sampling Variability. The Sampling Distribution of a Sample Mean. The Sampling Distribution of a Sample Proportion.

• Chapter 9: Estimation Using A Single Sample. (4 days)
Point Estimation. A Large Sample Confidence Interval for a Population Proportion. A Confidence Interval for a Population Mean. Interpreting the Results of Statistical Analyses.

• Chapter 10: Hypothesis Testing Using A Single Sample. (6 days)
Hypotheses and Test Procedures. Errors in Hypothesis Testing. Large-Sample Hypothesis Tests for a Population Proportion. Hypothesis Tests for a Population Mean. Power and Probability of Type II Error (Optional). Interpreting the Results of Statistical Analyses.
• Chapter 11: Comparing Two Populations or Treatments. (4 days)
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. (2 days)
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. (2 days)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. (2 days)
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. (2 days)
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.

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