Course Overview: STAT-I 301 Spring 2026

This course syllabus outlines the sequence of topics for a college-level statistics course, covering foundational concepts through advanced inferential techniques. The schedule is organized by week, with each lecture focusing on a specific statistical topic. Below is a structured summary of the main topics, subtopics, and their academic context, suitable for exam preparation.

1. Introduction to Statistics

1.1 Types of Data

Statistics begins with understanding the types of data collected and analyzed.

• Qualitative (Categorical) Data: Data that describes qualities or categories (e.g., gender, color).

• Quantitative Data: Data that represents numerical values (e.g., height, weight).

• Discrete Data: Countable values (e.g., number of students).

• Continuous Data: Measurable values within a range (e.g., temperature).

• Example: Survey responses about favorite ice cream flavor (qualitative); number of scoops sold (quantitative).

1.2 Collecting Sample Data

Proper data collection is essential for valid statistical analysis.

• Population: The entire group of interest.

• Sample: A subset of the population used for analysis.

• Sampling Methods: Random, stratified, cluster, systematic.

• Example: Randomly selecting 100 students from a university to survey.

2. Exploring Data with Tables and Graphs

2.1-2.3 Exploring Data

Visual and tabular methods help summarize and interpret data.

• Frequency Tables: Organize data into categories and counts.

• Histograms: Graphical representation of data distribution.

• Boxplots: Visualize spread and identify outliers.

• Example: Creating a histogram of exam scores to observe distribution.

3. Describing, Exploring, and Comparing Data

3.1 Measures of Center

Central tendency describes the "center" of a data set.

• Mean: Arithmetic average.

• Median: Middle value when data is ordered.

• Mode: Most frequently occurring value.

• Example: Calculating the mean score of a class.

3.2-3.3 Measures of Spread and the Z Score

Spread measures describe variability in data.

• Range: Difference between maximum and minimum values.

• Variance: Average squared deviation from the mean.

• Standard Deviation: Square root of variance.

• Z Score: Standardized value.

• Example: Calculating the z-score for a student’s test result.

4. Probability

4.1-4.2 Basic Probability

Probability quantifies the likelihood of events.

• Probability:

• Sample Space: All possible outcomes.

• Event: A subset of the sample space.

• Example: Probability of rolling a 3 on a six-sided die:

4.2-4.3 Rules of Probability

Rules help calculate probabilities for combined events.

• Addition Rule:

• Multiplication Rule: (if independent)

• Complement Rule:

• Example: Probability of drawing a red or a face card from a deck.

5. Discrete Probability Distributions

5.1 Discrete Random Variables

Discrete random variables take countable values.

• Probability Distribution: Assigns probabilities to each possible value.

• Expected Value:

• Example: Number of heads in three coin tosses.

5.2 The Binomial Distribution

The binomial distribution models the number of successes in fixed trials.

• Binomial Formula:

• Parameters: n = number of trials, p = probability of success.

• Example: Probability of getting 2 heads in 5 coin tosses.

6. Normal Probability Distributions

6.1 The Normal Distribution

The normal distribution is a continuous, symmetric distribution.

• Probability Density Function:

• Properties: Mean = median = mode; bell-shaped curve.

• Example: Heights of adult males.

6.2 Application to the Normal Distribution

Applications include calculating probabilities and percentiles.

• Z-table: Used to find probabilities for standard normal values.

• Example: Probability a student scores above 85 if mean is 80, SD is 5.

6.4 The Central Limit Theorem (CLT)

The CLT states that the sampling distribution of the sample mean approaches normality as sample size increases.

• CLT Formula:

• Example: Average weight of 30 randomly selected apples.

6.6 Normal Approximation to the Binomial Distribution

For large n, the binomial can be approximated by the normal distribution.

• Conditions: np > 5 and n(1-p) > 5

• Example: Probability of at least 40 successes in 100 trials.

7. Estimating Parameters and Determining Sample Sizes

7.2 Confidence Intervals (CI) for the Mean

Confidence intervals estimate population parameters.

• CI using z-table:

• CI using t-table:

• Example: Estimating average exam score with 95% confidence.

7.1 CI for Proportion (Large Samples)

Confidence intervals for proportions use the normal approximation.

• Formula:

• Example: Estimating proportion of students who pass an exam.

8. Hypothesis Testing

8.1 Basics of Hypothesis Testing

Hypothesis testing evaluates claims 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.

• Example: Testing if average height differs from 170 cm.

8.3 Small Sample Hypothesis Tests for the Mean

For small samples, t-tests are used.

• t-test Formula:

• Example: Testing mean exam score with n = 12.

8.2 One Sample Hypothesis Test for Proportions

Tests for proportions use the z-test.

• z-test Formula:

• Example: Testing if pass rate is above 60%.

9. Inferences from Two Samples

9.1 HT and CI for Comparing Two Proportions

Comparing proportions between two groups.

• CI Formula:

• Example: Comparing pass rates between two classes.

9.2 HT and CI for Comparing Two Means

Comparing means between two independent samples.

• CI Formula:

• Example: Comparing average scores between two groups.

9.3 Matched Pairs Comparison for the Means

Used when samples are paired (e.g., before and after measurements).

• Paired t-test Formula:

• Example: Comparing blood pressure before and after treatment.

10. Correlation and Regression

10.1 Correlated Data

Correlation measures the strength and direction of linear relationships.

• Pearson Correlation Coefficient:

• Example: Relationship between hours studied and exam score.

10.2 Regression

Regression models the relationship between variables.

• Simple Linear Regression Equation:

• Least Squares Estimation: Minimizes sum of squared residuals.

• Example: Predicting exam score based on study hours.

10.3 Rank Correlation

Rank correlation measures association between ranked variables.

• Spearman's Rank Correlation:

• Example: Ranking students by test scores and participation.

Course Logistics and Assignments

• Quizzes (Q): Weekly assessments on lecture material.

• Real World Problems (RW): Applied assignments due Fridays.

• Mile Marker Projects (MM): Major projects due Mondays.

• Examinations: Scheduled at the Testing Center with specified windows.

Summary Table: Course Topics by Week

Additional info: This summary expands brief syllabus points into academic explanations, formulas, and examples for self-contained study notes.