Course Overview

Introduction to Elementary Statistics

This course provides a comprehensive introduction to statistics, focusing on estimation, hypothesis testing, probability, and data analysis. It is designed for students in biological, health, social sciences, and communications, emphasizing practical applications and quantitative reasoning.

• Textbook: Michael Sullivan III, Statistics: Informed Decisions Using Data, 7th edition.

• Homework: Online assignments via MyLab Statistics.

• Exams: Two midterms and a final exam.

• Grading: Final exam (25%), midterms (15% each), homework (40%), attendance/participation (5%).

Weekly Topics and Key Concepts

Week 1: Collecting Data & Sampling Methods

Understanding how data is collected is fundamental to statistics. This week covers sampling techniques and sources of bias.

• Simple Random Sampling: Every member of the population has an equal chance of being selected.

• Other Sampling Methods: Includes stratified, cluster, systematic, and convenience sampling.

• Bias: Systematic error introduced by sampling methods.

• Correlation vs. Causation: Correlation does not imply causation; lurking variables may affect results.

• Lurking Variables: Variables not included in the study that may influence the outcome.

Example: Selecting students randomly from a university to survey opinions avoids bias compared to surveying only students from one department.

Week 2: Describing Data with Tables and Graphs

Visual representation of data helps in understanding distributions and patterns.

• Frequency Distributions: Tables showing how often each value occurs.

• Pie Charts: Circular charts representing proportions.

• Histograms: Bar graphs showing frequency of data intervals.

• Other Graphs: Bar charts, line graphs, etc.

Example: Creating a histogram to display the distribution of exam scores.

Week 3: Describing Data Numerically

Numerical summaries provide insight into the central tendency and variability of data.

• Mean: Arithmetic average.

• Median: Middle value when data is ordered.

• Mode: Most frequently occurring value.

• Range: Difference between maximum and minimum values.

• Variance: Measure of spread.

• Standard Deviation: Square root of variance.

• Interquartile Range (IQR): Difference between the 75th and 25th percentiles.

• Percentiles: Values below which a certain percentage of data falls.

Example: Calculating the mean and standard deviation of heights in a sample.

Week 4: Scatter Plots & Regression

Scatter plots and regression lines are used to analyze relationships between two variables.

• Scatter Plot: Graph of paired data points.

• Least-Squares Regression Line: Line that minimizes the sum of squared residuals.

• Correlation: Measure of linear relationship between variables.

• Limitations: Linear models may not fit all data; beware of extrapolation.

Example: Plotting hours studied vs. exam score and fitting a regression line.

Week 5: Introduction to Probability

Probability quantifies uncertainty and is foundational for inferential statistics.

• Frequency Interpretation: Probability as long-run relative frequency.

• Conditional Probability: Probability of event A given event B.

• Multiplication Rule:

Example: Calculating the probability of drawing two aces from a deck.

Week 7: Binomial Distribution & Discrete Random Variables

Discrete probability distributions describe the likelihood of outcomes for discrete random variables.

• Binomial Distribution: Probability of k successes in n trials.

• Discrete Random Variable: Variable that takes on countable values.

Example: Probability of getting 3 heads in 5 coin tosses.

Week 8: Normal Distribution & Continuous Random Variables

The normal distribution is a continuous probability distribution important in statistics.

• Normal Probability Density Function:

• Standard Normal Distribution: Mean 0, standard deviation 1.

• Area Under Curve: Represents probability.

Example: Using z-tables to find probabilities for exam scores.

Week 9: Sampling Distributions

Sampling distributions describe the distribution of statistics (like means or proportions) from repeated samples.

• Central Limit Theorem: Sampling distribution of the mean approaches normality as sample size increases.

• Sample Proportion Distribution: Often approximately normal for large samples.

Example: Distribution of sample means from repeated samples of student heights.

Week 10: Confidence Intervals

Confidence intervals estimate population parameters with a specified level of confidence.

• Population Proportion:

• Population Mean: (or t* if σ unknown)

Example: Estimating the average height of students with 95% confidence.

Week 11-12: Hypothesis Testing

Hypothesis testing is used to make inferences about population parameters.

• Null Hypothesis (H0): Statement of no effect or difference.

• Alternative Hypothesis (Ha): Statement of effect or difference.

• Test Statistic: Calculated from sample data.

• p-value: Probability of observing data as extreme as sample, assuming H0 is true.

• Population Proportion Test:

• Population Mean Test:

Example: Testing if the average exam score differs from 75.

Week 13-14: Two-Sample Inference

Comparing two populations involves testing differences in means or proportions.

• Independent Samples: Samples with no relationship.

• Dependent Samples: Paired or matched samples.

• Two-Proportion Test:

• Two-Mean Test:

Example: Comparing average heights between two classes.

Grading Breakdown

Semester Grade Distribution

Academic Conduct and Use of Technology

• Academic Misconduct: Plagiarism and cheating are strictly prohibited.

• Technology Use: Laptops and devices should be used only for course-related activities.

Summary Table: Weekly Topics and Corresponding Chapters

Additional info: The syllabus aligns closely with the standard introductory statistics curriculum, covering all major topics from data collection to hypothesis testing and regression. Students are encouraged to use R and RStudio for data analysis.