STAT C1000: Introduction to Statistics – Course Syllabus and Topical Outline Study Guide

Course Overview

Introduction to Statistics

This course provides a comprehensive introduction to statistics, covering both descriptive and inferential methods. Students will learn to summarize, analyze, and interpret data using a variety of statistical techniques, including probability distributions, hypothesis testing, regression, and analysis of variance. Applications span multiple disciplines such as business, social sciences, psychology, life sciences, health sciences, and education.

• Textbook: Elementary Statistics (14th edition) by Mario F. Triola

• Required Materials: Canvas, BC email, MyLab Statistics access, basic calculator

• Class Meetings: General Science 13, MW 1:00-3:05 PM

Student Learning Outcomes

• Translate application problems using inferential data analysis techniques and interpret solutions.

• Apply probability and probability distributions to solve problems.

• Demonstrate knowledge of descriptive statistics and communicate concepts clearly.

Course Objectives

• Distinguish among scales of measurement and interpret data in tables and graphs.

• Apply concepts of sample space and probability.

• Calculate measures of central tendency and variation; identify data collection methods.

• Calculate mean and variance of discrete distributions; use normal and t-distributions.

• Differentiate between sample and population distributions; understand the Central Limit Theorem.

• Construct and interpret confidence intervals; determine statistical significance and p-values.

• Identify hypothesis testing concepts, including Type I and II errors.

• Formulate and interpret hypothesis tests for one and two populations.

• Use linear regression and ANOVA for estimation and inference.

Topical Outline

A. Introduction

• Basic Terms and Definitions: Population, Sample, Parameter, Statistic

• Descriptive vs. Inferential Statistics: Descriptive statistics summarize data; inferential statistics draw conclusions from data.

• Levels/Scales of Measurement: Nominal, Ordinal, Interval, Ratio

• Quantitative vs. Qualitative Variables: Quantitative variables are numerical; qualitative variables are categorical.

• Discrete and Continuous Variables: Discrete variables take countable values; continuous variables take any value within a range.

B. Experimental Design and Data Collection

• Research Methods: Observational studies, experiments

• Measurement Error: Difference between measured and true value

• Types of Designs: Randomized, matched pairs, block designs

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

C. Graphical Displays of Univariate Data

• Tabular and Graphical Techniques: Frequency tables, bar charts, histograms, pie charts

• Shapes of Distributions: Symmetric, skewed, uniform, bimodal

D. Measurements of Location and Position

• Measurements of Location: Mean, median, mode

• Measurements of Position: Percentiles, quartiles

• Box and Whisker Plots: Visual representation of the five-number summary

E. Measurements of Variability

• Range: Difference between maximum and minimum values

• Variance and Standard Deviation: Measures of spread; variance is the average squared deviation, standard deviation is its square root

• Five-number Summary: Minimum, Q1, Median, Q3, Maximum

• Empirical Rule: For normal distributions, about 68% of data falls within 1 SD, 95% within 2 SD, 99.7% within 3 SD

• Chebyshev’s Rule: Applies to any distribution; at least $(1 - \frac{1}{k^2})$ of data falls within $k$ standard deviations

F. Probability

• Simulation: Using models to estimate probabilities

• Empirical Probability: Based on observed data

• Theoretical Probability: Based on mathematical reasoning

• Probability of Events: $P(A) = \frac{n(A)}{n(S)}$

• Law of Large Numbers: As trials increase, empirical probability approaches theoretical probability

• Sample Spaces: Set of all possible outcomes

• Odds: Ratio of favorable to unfavorable outcomes

• Rules of Probability: Addition, multiplication, complement rules

G. Random Variables and Probability Distributions

• Random Variables: Variable whose value is determined by chance

• Discrete Probability Distributions: Probability mass function, mean, variance

• Expected Value: $E(X) = \sum x_i P(x_i)$

H. Binomial Probability Distribution

• Binomial Experiment: Fixed number of trials, two outcomes, independent trials, constant probability

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

• Mean and Standard Deviation: $\mu = np$, $\sigma = \sqrt{np(1-p)}$

• Histograms: Visualize binomial probabilities

I. Normal Distribution

• Normal Probability Density Function: $f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

• Properties: Symmetric, bell-shaped, mean = median = mode

• Finding Probabilities: Use z-scores: $z = \frac{x - \mu}{\sigma}$

• Applications: Standardized testing, quality control

• Percentiles: Value below which a given percentage of observations fall

J. Sampling Distributions

• Sampling Distribution of Sample Statistic: Distribution of a statistic over repeated samples

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

• Sampling Distribution of Sample Proportion: $\mu_p = p$, $\sigma_p = \sqrt{\frac{p(1-p)}{n}}$

K. Confidence Intervals for Univariate Data

• Estimation of Proportions: $\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

• Estimation of the Mean: $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$ (or $t^*$ if $\sigma$ unknown)

• Sample Size: $n = \left(\frac{z^* \sigma}{E}\right)^2$

• Confidence Interval for the Median: Nonparametric methods may be used

L. Univariate Hypothesis Testing

• Logic: Test a claim about a population parameter

• Type I Error: Rejecting a true null hypothesis ($\alpha$)

• Type II Error: Failing to reject a false null hypothesis ($\beta$)

• One- or Two-Tailed Tests: Directional or non-directional hypotheses

• Hypothesis Tests for Mean or Proportion: z-test, t-test, proportion test

• Relationship between Hypothesis Testing and Confidence Intervals: If CI does not contain null value, reject $H_0$

• Statistical Analysis Using Technology: SPSS, Excel, Minitab, calculators

M. Comparing Two Population Parameters

• Dependent vs. Independent Samples: Paired vs. unpaired data

• Independent Samples: Comparison of means, variances, proportions

• t-tests for Two Populations: $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$

• Dependent Samples: Inferences concerning mean difference

• Confidence Intervals for Differences: For means and proportions

• Statistical vs. Practical Significance: Statistical significance may not imply practical importance

• Nonparametric Tests: Wilcoxon Rank Sum, Sign Test

• Applications: Data from various disciplines

N. Analysis of Variance (ANOVA)

• Logic and Assumptions: Compare means across multiple groups

• One-Way ANOVA: $F = \frac{\text{Between-group variance}}{\text{Within-group variance}}$

• Kruskal–Wallis Test: Nonparametric alternative to ANOVA

O. Categorical Data Analysis

• Chi-Squared Goodness of Fit Test: $\chi^2 = \sum \frac{(O - E)^2}{E}$

• Test of Independence: Assess association between categorical variables

P. Correlation and Simple Linear Regression

• Scatterplots and Correlation: Visualize and measure linear association

• Causation vs. Association: Correlation does not imply causation

• Simple Linear Regression: $y = \beta_0 + \beta_1 x$

Q. Optional Topics

• Odds Ratios: Measure of association for categorical data

• Fisher’s Least Square Difference: Post-hoc test after ANOVA

• Inferences Concerning Correlation: Test significance of correlation coefficient

• Confidence Interval for Correlation Coefficient: Use Fisher transformation

• Spearman’s Rank Correlation: Nonparametric measure of association

Course Schedule

Week	Topics	Assignments
1	Syllabus, Ch. 1, Ch. 2	Lab 1
2	Ch. 3	Lab 2, Homework 1, Quiz 1
3	Ch. 4	Homework 2, Quiz 2, Exam I (Ch. 1-3)
4	Ch. 4	Lab 3
5	Ch. 5	Lab 4, Homework 3, Quiz 3
6	Ch. 6	Homework 4, Quiz 4, Exam II (Ch. 4-5)
7	Ch. 6	Lab 5
8	Ch. 7	Lab 6, Homework 5, Quiz 5
9	Ch. 8	Homework 6, Quiz 6, Exam III (Ch. 6-7)
10	Ch. 8	Lab 7
11	Ch. 9	Lab 8, Homework 7, Quiz 7
12	Ch. 9	Lab 9, Homework 8, Quiz 8
13	Ch. 10	Homework 9, Quiz 9, Exam IV (Ch. 8-9)
14	Ch. 10	Lab 10, Homework 10, Quiz 10
15	Ch. 10	Homework 11, Quiz 11, Review
16	Final Exam

Grading Breakdown

Assessment	Points
4 Semester Exams	400
1 Cumulative Final	250
10 Homeworks	100
10 Quizzes	100
15 Labs	150
Total	1000

Grade Scale:

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

Tips for Success

• Invest appropriate time; expect several hours per week outside class.

• Prepare for class; review notes and attempt homework independently.

• Seek help from instructor or peer tutoring as needed.

Additional Info

• Peer tutoring and disability services are available for support.

• Academic integrity is strictly enforced.

• Important dates for drops, holidays, and final exam are provided in the syllabus.