Statistics Course Syllabus and Topical Outline – Kankakee Community College (MATH 1774)

Statistics Course Syllabus and Topical Outline

Course Overview

This course provides an introduction to the fundamental concepts and methods of statistics, focusing on data collection, analysis, and interpretation. Students will learn to apply statistical reasoning to real-world problems, utilizing both descriptive and inferential techniques. The course emphasizes the use of technology and statistical software for data analysis.

Course Objectives

• Organize data using frequency distributions and graphs.

• Distinguish between different types of studies and sampling methods.

• Summarize data numerically and graphically.

• Perform calculations associated with measures of central tendency and spread.

• Understand and apply probability rules and distributions.

• Construct confidence intervals and perform hypothesis tests.

• Interpret statistical results and make informed decisions.

Topical Outline

A. Data Collection

• Introduction to the Practice of Statistics: Understanding the role of statistics in various fields and the importance of data-driven decision making.

• Observational Studies vs. Designed Experiments:

  • Observational studies involve observing subjects without intervention.

  • Designed experiments involve manipulating variables to determine effects.

• 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.

• Sources of Bias: Bias can arise from poor sampling methods, nonresponse, or measurement errors.

B. Organizing and Summarizing Data

• Organizing Qualitative Data: Using frequency tables and bar charts to summarize categorical data.

• Organizing Quantitative Data:

  • Popular displays include histograms, stem-and-leaf plots, and dot plots.

• Graphical Misrepresentation: Recognizing misleading graphs and charts.

C. Numerically Summarizing Data

• Measures of Central Tendency:

  • Mean: Arithmetic average.

  • Median: Middle value.

  • Mode: Most frequent value.

• Measures of Dispersion:

  • Range: Difference between highest and lowest values.

  • Variance and Standard Deviation: Measures of spread around the mean.

• Measures of Position:

  • Percentiles, quartiles, and z-scores.

• Identifying Outliers: Using the IQR method or z-scores to detect unusual data points.

• Summarizing Data from Grouped Data: Calculating estimates of mean and variance from frequency tables.

D. Describing the Relation Between Two Variables

• Scatter Diagrams and Correlation: Visualizing and quantifying the relationship between two quantitative variables.

• Least-Squares Regression: Fitting a line to data to model the relationship between variables.

• Diagnostics for Least-Squares Regression: Checking assumptions and identifying influential points.

• Contingency Tables and Association: Analyzing relationships between categorical variables.

E. Probability

• Probability Rules:

  • Basic rules: Addition and multiplication rules.

  • Complement rule: $P(A^c) = 1 - P(A)$

• Counting Techniques:

  • Permutations: $n!$

  • Combinations: $\binom{n}{r}$

• Conditional Probability and Independence: $P(A|B) = \frac{P(A \cap B)}{P(B)}$

• Bayes' Theorem: $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$

F. Discrete Probability Distributions

• Random Variables: Variables whose values are determined by chance.

• Binomial Probability Distribution: $P(X = k) = \binom{n}{k}p^k(1-p)^{n-k}$

• Mean and Standard Deviation of Discrete Distributions: $\mu = \sum xP(x)$, $\sigma = \sqrt{\sum (x-\mu)^2P(x)}$

G. The Normal Probability Distribution

• Properties of the Normal Distribution: Symmetrical, bell-shaped, defined by mean $\mu$ and standard deviation $\sigma$.

• Standard Normal Distribution: $Z = \frac{X - \mu}{\sigma}$

• Assessing Normality: Using normal probability plots and tests for normality.

H. Sampling Distributions

• Distribution of the Sample Mean: Central Limit Theorem: For large $n$, the sampling distribution of the mean is approximately normal.

• Distribution of the Sample Proportion: For large $n$, the sampling distribution of the proportion is approximately normal.

I. Estimating the Value of a Parameter

• Estimating a Population Mean: Confidence interval: $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

• Estimating a Population Proportion: Confidence interval: $\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

• Estimating a Population Standard Deviation: Using the chi-square distribution.

• Putting It Together: Which Procedure Do I Use? Guidelines for selecting the appropriate estimation method.

J. Hypothesis Tests Regarding a Parameter

• The Language of Hypothesis Testing: Null hypothesis ($H_0$), alternative hypothesis ($H_a$), significance level ($\alpha$), p-value.

• Hypothesis Tests for a Population Mean: One-sample z-test and t-test.

• Hypothesis Tests for a Population Proportion: One-sample z-test for proportions.

• Hypothesis Tests for a Population Standard Deviation: Chi-square test.

• Putting It Together: Which Procedure Do I Use? Decision tree for hypothesis testing.

K. Inference on Two Population Parameters

• Inference about Two Means, Independent Samples: Two-sample t-test.

• Inference about Two Means, Dependent Samples: Paired t-test.

• Inference about Two Population Proportions: Two-proportion z-test.

L. Inference on Categorical Data

• Chi-Square Test for Independence: Tests association between categorical variables.

• Test of Homogeneity of Proportions: Compares proportions across groups.

M. Comparing Three or More Means

• One-Way Analysis of Variance (ANOVA): Tests for differences among group means.

N. Inference on the Least-Squares Regression Model

• Inference for Slope: Testing if the slope of the regression line is significantly different from zero.

• Multiple Regression: Extending regression analysis to more than one predictor variable.

Example Table: Types of Sampling Methods

Sampling Method	Description	Example
Simple Random Sampling	Every member has an equal chance of selection	Drawing names from a hat
Stratified Sampling	Population divided into subgroups, random sample from each	Sampling students from each grade level
Cluster Sampling	Population divided into clusters, entire clusters randomly selected	Randomly selecting classrooms and surveying all students in them
Systematic Sampling	Selecting every k-th member from a list	Surveying every 10th person on a list
Convenience Sampling	Sampling individuals who are easiest to reach	Surveying people at a mall

Additional info:

• This syllabus covers all major topics found in a standard college-level statistics course, matching the chapter titles provided in the prompt.

• Students are expected to use MyStatLab for homework and assignments.

• Course policies emphasize academic integrity, attendance, and the use of technology in statistics.