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

Course Overview

Introduction

This course, STAT 1000: Basic Statistical Analysis 1, provides a comprehensive introduction to the fundamental concepts and methods of statistics. The syllabus outlines the structure, topics, and expectations for students, emphasizing both theoretical understanding and practical application of statistical analysis.

Course Units and Topics

Unit 1: Examining Distributions

Understanding distributions is foundational in statistics, as it allows for the description and interpretation of data.

• Types of Variables: Quantitative (numerical) and 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.

• Numerical Summaries: Mean, median, mode, weighted mean, quartiles, percentiles, interquartile range, variance, standard deviation.

• Outlier Detection: 1.5 × IQR rule for suspected outliers, boxplots.

Example: A histogram of exam scores can reveal whether the distribution is symmetric or skewed, and boxplots can help identify outliers.

Unit 2: Correlation & Regression

This unit explores relationships between variables, focusing on quantifying and modeling associations.

• 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 and leverage points can affect regression results.

• Explanatory vs. Response Variables: Identifying dependent and independent 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: Predicting house prices based on square footage using linear regression.

Unit 3: Sampling & Experimental Design

Proper sampling and experimental design are crucial for valid statistical inference.

• Population and Sample: Definitions and distinctions.

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

• Bias: Voluntary response bias, nonresponse bias.

• Experimental Design: Observational vs. experimental studies, factors, treatments, control groups, randomization, replication, blocking.

Example: Randomly selecting students from different faculties to participate in a survey.

Unit 4: Density Curves & Normal Distributions

This unit introduces continuous probability distributions, with a focus on the normal distribution.

• Continuous Variables: Variables that can take any value within a range.

• Density Curves: Mathematical models for distributions.

• Normal Distribution: Symmetric, bell-shaped curve defined by mean ($\mu$) and standard deviation ($\sigma$).

• Standardization: Converting values to z-scores.

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

Formula: $z = \frac{x - \mu}{\sigma}$ Example: Calculating the probability that a randomly selected student’s height falls within one standard deviation of the mean.

Unit 5: Probability & Sampling Distributions of the Sample Mean

Probability theory underpins statistical inference, and sampling distributions describe the behavior of sample statistics.

• Probability: Definitions, sample space, probability rules.

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

Formula: $\text{Central Limit Theorem:} \quad \bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$ Example: The mean of repeated samples from a population will be approximately normally distributed if the sample size is large enough.

Unit 6: Confidence Intervals

Confidence intervals provide a range of plausible values for population parameters.

• Estimating Population Mean: Using sample data to estimate unknown parameters.

• Margin of Error: Quantifies uncertainty in estimation.

• Effect of Sample Size: Larger samples yield narrower intervals.

Formula: $\text{Confidence Interval:} \quad \bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$ Example: Estimating the average time students spend studying per week with 95% confidence.

Unit 7: Hypothesis Testing

Hypothesis testing is a formal procedure for making inferences about population parameters.

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

• Test Statistics: Calculated from sample data to assess evidence against $H_0$.

• p-value: Probability of observing data as extreme as the sample, assuming $H_0$ is true.

Formula: $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$ Example: Testing whether the mean exam score differs from a hypothesized value.

Unit 8: Inference for the Population Mean when σ is Unknown

When population standard deviation is unknown, the t-distribution is used for inference.

• t-distribution: Similar to normal but with heavier tails, used when estimating mean with unknown $\sigma$.

• Confidence Intervals and Hypothesis Tests: Adjusted for sample standard deviation.

Formula: $\text{Confidence Interval:} \quad \bar{x} \pm t^* \frac{s}{\sqrt{n}}$ Example: Estimating the mean income of a population when only sample data is available.

Unit 9: Sampling Distributions and Inference for Proportions

This unit covers estimation and hypothesis testing for population proportions.

• Sample Proportion: $\hat{p} = \frac{x}{n}$

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

• Hypothesis Testing for Proportion: Comparing observed proportion to hypothesized value.

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

Course Schedule Table

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: Examining Distributions	Worksheet 2
4	Jan. 27 - Jan. 30	Quiz 1		Assignment 2 Released Jan. 27, Due Feb. 3
5	Feb. 3 - Feb. 6	Tutorial 3: Correlation & Regression	Worksheet 3
6	Feb. 10 - Feb. 13	Quiz 2		Assignment 3 Released Feb. 10, Due Feb. 17
7	Feb. 24 - Feb. 27	Tutorial 4: Sampling & Experimental Design	Worksheet 4	Assignment 4 Released Feb. 24, Due Mar. 2
8	Mar. 2 - Mar. 5	Quiz 3
9	Mar. 9 - Mar. 12	No Tutorial
10	Mar. 16 - Mar. 19	Tutorial 5: Density Curves & Normal Distributions	Worksheet 5	Assignment 5 Released Mar. 16, Due Mar. 23
11	Mar. 23 - Mar. 26	Quiz 4
12	Mar. 30 - Apr. 2	Tutorial 6: Probability & Sampling Distributions	Worksheet 6	Assignment 6 Released Mar. 30, Due Apr. 6

Evaluation

• iClicker Questions/Participation: 5%

• Tutorial Worksheets: 15%

• Assignments & Quizzes: 25%

• Midterm Test: 25%

• Final Examination: 30%

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: Strict policies against plagiarism and unauthorized collaboration.

• Support: Statistics Help Centre available for student assistance.

Additional info: The syllabus covers all major topics listed in the Statistics college course chapter titles, including data collection, descriptive statistics, probability, distributions, sampling, confidence intervals, hypothesis testing, correlation, and regression.