Introductory Statistics (MATH 125) Syllabus and Study Guide

Course Overview

This syllabus outlines the structure, objectives, and policies for MATH 125: Introductory Statistics at Malcolm X College, City Colleges of Chicago. The course covers foundational concepts in statistics, including data analysis, probability, distributions, hypothesis testing, and statistical inference, with an emphasis on real-world applications and critical thinking.

Course Objectives

• Develop statistical reasoning as it relates to contextual (real-world) scenarios.

• Apply statistical techniques to data from various representations.

• Interpret statistical results appropriately (verbally and in writing).

• Use technology to perform statistical computations and explore statistical concepts.

Student Learning Outcomes

• Identify and interpret data/variable types, study designs, assumptions, and biases using appropriate terminology and various data representations.

• Organize, summarize, and interpret raw data using descriptive statistics and graphical methods (e.g., frequency distributions, histograms, boxplots).

• Calculate and interpret measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation).

• Apply basic probability rules and concepts, including the addition and multiplication rules, and conditional probability.

• Work with discrete probability distributions (e.g., binomial) and continuous distributions (e.g., normal distribution).

• Construct and interpret confidence intervals for population means and proportions.

• Conduct and interpret hypothesis tests for one and two samples, including tests for means and proportions.

• Analyze correlation and regression between variables, interpret correlation coefficients, and use regression equations for prediction.

• Perform and interpret chi-square tests for categorical data using contingency tables (tests of independence, goodness-of-fit, homogeneity).

• Demonstrate working knowledge of computational software for organizing data, generating statistical graphics, and performing calculations.

Topical Outline

Week	Topic	Key Concepts
1-2	Introduction to Statistics	Statistical reasoning, types of data, sampling methods
3-4	Descriptive Statistics	Measures of central tendency and dispersion, graphical summaries
5-7	Probability	Basic probability rules, conditional probability, addition/multiplication rules
8-9	Discrete Probability Distributions	Binomial distribution, expected value, variance
10-11	Normal Probability Distributions	Standard normal distribution, z-scores, applications
12	Confidence Intervals	Confidence intervals for means and proportions
13-14	Hypothesis Testing	One-sample and two-sample tests for means and proportions
15	Correlation and Regression	Scatterplots, correlation coefficient, regression line
16	Chi-Square Tests and F-Distribution	Contingency tables, goodness-of-fit, independence tests

Key Definitions and Concepts

Descriptive Statistics

• Mean ($\bar{x}$): The arithmetic average of a set of values. $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

• Median: The middle value when data are ordered.

• Mode: The value that appears most frequently in a data set.

• Variance ($s^2$): The average squared deviation from the mean. $s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$

• Standard Deviation ($s$): The square root of the variance. $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

Probability

• Probability of an event ($P(A)$): The likelihood that event A occurs. $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Addition Rule: For two events A and B: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

• Multiplication Rule: For independent events A and B: $P(A \cap B) = P(A) \times P(B)$

Discrete Probability Distributions

• Binomial Distribution: Probability of x successes in n independent Bernoulli trials. $P(X = x) = {n \choose x} p^x (1-p)^{n-x}$

Normal Probability Distributions

• Standard Normal Distribution: A normal distribution with mean 0 and standard deviation 1.

• Z-score: Number of standard deviations a value is from the mean. $z = \frac{x - \mu}{\sigma}$

Confidence Intervals

• Confidence Interval for Mean (known $\sigma$): $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

• Confidence Interval for Proportion: $\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Hypothesis Testing

• Null Hypothesis ($H_0$): The statement being tested, usually a statement of no effect or no difference.

• Alternative Hypothesis ($H_a$): The statement we want to test for evidence in favor of.

• Test Statistic (z or t): Measures how far the sample statistic is from the null hypothesis value. $z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$

• P-value: The probability of observing a test statistic as extreme as, or more extreme than, the observed value under $H_0$.

Correlation and Regression

• Correlation Coefficient ($r$): Measures the strength and direction of a linear relationship between two variables. $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$

• Regression Line: The best-fitting straight line through a scatterplot of data. $y = a + bx$

Chi-Square Tests

• Chi-Square Statistic ($\chi^2$): Used to test relationships between categorical variables. $\chi^2 = \sum \frac{(O - E)^2}{E}$ where $O$ = observed frequency, $E$ = expected frequency

Grading Policy

• Homework: 25%

• Quizzes: 30%

• Exams: 45%

Letter Grade	Percentage
A	90% - 100%
B	80% - 89%
C	70% - 79%
D	60% - 69%
F	Below 60%

Course Policies and Resources

• Attendance and participation are required for success.

• Assignments must be submitted on time; late work may not be accepted.

• Academic integrity is strictly enforced.

• Support services are available, including tutoring, advising, and wellness resources.

Additional info:

• This syllabus provides a comprehensive overview of the course structure and expectations. For detailed explanations of each statistical topic, refer to the course textbook: Elementary Statistics by Ron Larson (Pearson).

• Students are encouraged to use statistical software and calculators for assignments and exams.