STAT 1000: Basic Statistical Analysis 1 – Syllabus and Course Outline Study Guide

Course Overview

Introduction to Basic Statistical Analysis

This course provides a comprehensive introduction to the fundamental concepts and methods of statistics, focusing on data collection, description, probability, distributions, and inferential techniques. The syllabus outlines the structure, evaluation, and key topics covered throughout the term, preparing students for further study and practical application in statistics.

Course Structure and Evaluation

Evaluation Components

• iClicker Questions/Participation: 5%

• Tutorial Worksheets: 15%

• Assignments/Quizzes: 25%

• Midterm Test: 25%

• Final Examination: 30%

Students are assessed through a combination of participation, assignments, quizzes, a midterm, and a final exam. Tutorials and assignments are designed to reinforce statistical concepts and problem-solving skills.

Course Outline

Unit 1 – Examining Distributions

This unit introduces the foundational concepts for describing and summarizing data distributions.

• Types of Variables: Quantitative, categorical (nominal, ordinal)

• Graphical Methods: Dot plots, histograms, frequency distributions, time plots

• Describing Distributions: Shape (skewed, symmetric), center (mean, median), spread (range, variance, standard deviation, quartiles)

• Outliers: Identifying outliers using the 1.5 × IQR rule, boxplots

• Summary Statistics: Mean, median, mode, weighted mean, quartiles, percentiles, interquartile range, variance, standard deviation

Example: Constructing a histogram to visualize the distribution of exam scores and calculating the mean and standard deviation to summarize performance.

Unit 2 – Correlation & Regression

This unit explores relationships between variables using correlation and regression analysis.

• Correlation: Measures the strength and direction of linear relationships between two quantitative variables.

• Regression: Least squares regression line, prediction, residuals

• Scatterplots: Visual representation of bivariate data

• Influential Observations: Outliers, leverage, lurking variables

Formula: $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$

Example: Using regression to predict a student's final grade based on hours studied.

Unit 3 – Sampling & Experimental Design

This unit covers methods for collecting data and designing experiments to ensure valid statistical inference.

• Sampling Methods: Simple random sample, stratified sample, cluster sample, systematic sample

• Experimental Design: Observational study vs. experiment, factors, treatments, control groups, randomization, blinding

• Bias: Voluntary response bias, nonresponse bias, sampling error

Example: Designing a randomized controlled trial to test the effectiveness of a new medication.

Unit 4 – Density Curves & Normal Distributions

This unit introduces continuous probability distributions, focusing on the normal distribution and its properties.

• Continuous Variables: Density curves, area under the curve

• Normal Distribution: Standard normal distribution, $N(\mu, \sigma^2)$

• Empirical Rule: 68-95-99.7 rule for normal distributions

• Standardization: $z$-scores

Formula: $z = \frac{x - \mu}{\sigma}$

Example: Calculating the probability that a randomly selected student scores above 85 on a normally distributed exam.

Unit 5 – Probability & Sampling Distributions of the Sample Mean

This unit focuses on the principles of probability and the behavior of sample means.

• Probability Rules: Addition and multiplication rules, sample space, events

• Sampling Distributions: Distribution of sample means, Central Limit Theorem

Formula: $\mu_{\bar{x}} = \mu$, $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

Example: Using the Central Limit Theorem to estimate the probability that the average height of a sample of students exceeds a certain value.

Unit 6 – Confidence Intervals

This unit introduces methods for estimating population parameters using sample data.

• Confidence Interval for Mean: When population standard deviation is known or unknown

• Margin of Error: Effect of sample size, confidence level, standard deviation

Formula: $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

Example: Constructing a 95% confidence interval for the average time students spend studying per week.

Unit 7 – Hypothesis Testing

This unit covers the process of making inferences about populations based on sample data.

• Null and Alternative Hypotheses: $H_0$, $H_a$

• Test Statistics: $z$-test, $t$-test

• P-values: Interpreting statistical significance

Formula: $z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$

Example: Testing whether the mean exam score differs from a hypothesized value.

Unit 8 – Inference for the Population Mean when σ is unknown

This unit extends hypothesis testing and confidence intervals to cases where the population standard deviation is unknown.

• t-distribution: Used when $\sigma$ is unknown

• Confidence Interval: $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$

Example: Estimating the mean income of a population using sample data.

Unit 9 – Sampling Distributions and Inference for Proportions

This unit focuses on categorical data and inference for population proportions.

• Sampling Distribution of a Sample Proportion: $\hat{p}$

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

Example: Estimating the proportion of students who prefer online learning.

Course Schedule Table

Course Schedule Overview

The following table summarizes the weekly schedule, including tutorials, quizzes, and assignment due dates.

Week	Dates	Tutorials & Quizzes	Tutorial Worksheets	Assignments
1	Jan. 6 – Jan. 7	No tutorial
2	Jan. 13 – Jan. 16	Tutorial 1: Introduction	Worksheet 1	Assignment 1 Released Jan. 13, Due Jan. 20
3	Jan. 20 – Jan. 23	Tutorial 2: Describing Distributions	Worksheet 2
4	Jan. 27 – Jan. 30	Quiz 1	Worksheet 3	Assignment 2 Released Jan. 27, Due Feb. 3
5	Feb. 3 – Feb. 6	No Tutorial
6	Feb. 10 – Feb. 13	Quiz 2	Worksheet 4	Assignment 3 Released Feb. 10, Due Feb. 17
7	Feb. 24 – Feb. 27	Tutorial 3: Sampling	Worksheet 5	Assignment 4 Released Feb. 24, Due Mar. 2
8	Mar. 2 – Mar. 5	No Tutorial
9	Mar. 9 – Mar. 12	Quiz 3	Worksheet 6	Assignment 5 Released Mar. 9, Due Mar. 16
10	Mar. 16 – Mar. 19	No Tutorial
11	Mar. 23 – Mar. 26	Tutorial 4: Confidence Intervals	Worksheet 7	Assignment 6 Released Mar. 23, Due Mar. 30
12	Mar. 30 – Apr. 2	Quiz 4	Worksheet 8

Additional Information

• Software: R and RStudio are required for tutorials and assignments.

• Textbook: No required textbook; detailed notes and materials will be provided.

• Academic Integrity: Students must adhere to university policies regarding plagiarism and cheating.

• Support: Statistics Help Centre is available for additional assistance.

Additional info: The course outline closely matches the major topics in a college-level statistics curriculum, including data description, probability, distributions, sampling, confidence intervals, hypothesis testing, and regression.