Statistics 1000 & 54C: Course Syllabus and Study Guide

Statistics 1000 & Math 54C: Syllabus & Study Notes

Course Overview

This course covers the fundamentals of statistics, including data collection, descriptive and inferential statistics, probability distributions, hypothesis testing, and statistical reasoning. Math 54C serves as a support course, reinforcing prerequisite skills and concepts necessary for success in Statistics 1000.

• Course Title: Stat C1000, Elementary Statistics & Math 54C, Statistics & Support

• Instructor: Ebrahim Jahangard

• Textbook: Statistics: Informed Decisions Using Data by Michael Sullivan III, 7th Edition

• Prerequisite: Completion of Math 20, Math 18, Math 49, Math 50, or equivalent

Main Topics

1. Introduction to Statistics

Statistics is the science of collecting, analyzing, interpreting, and presenting data. It is essential for making informed decisions in various fields.

• Definition: Statistics involves methods for gathering, organizing, summarizing, and drawing conclusions from data.

• Branches: Descriptive statistics (summarizing data) and inferential statistics (drawing conclusions from data).

• Example: Using survey data to estimate the average income of a population.

2. Data Collection and Sampling

Proper data collection is crucial for valid statistical analysis. Sampling methods determine how representative the data is of the population.

• Random Sampling: Every member of the population has an equal chance of being selected.

• Simple Random Sample: A sample chosen in such a way that every possible sample of the same size has an equal chance of being selected.

• Other Sampling Methods: Stratified, cluster, systematic, and convenience sampling.

• Example: Selecting 100 students at random from a college for a survey.

3. Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set.

• Measures of Central Tendency: Mean, median, and mode.

• Measures of Variation: Range, variance, and standard deviation.

• Measures of Position: Percentiles and quartiles.

• Example: Calculating the average test score in a class.

• Formula for Mean: $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

• Formula for Standard Deviation: $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

4. Probability and Probability Distributions

Probability quantifies the likelihood of events occurring. Probability distributions describe how probabilities are distributed over values of a random variable.

• Probability: A measure between 0 and 1 indicating the chance of an event.

• Discrete Distributions: Binomial, Poisson.

• Continuous Distributions: Normal distribution.

• Example: Probability of flipping a coin and getting heads is 0.5.

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

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

5. Inferential Statistics

Inferential statistics use sample data to make generalizations about a population.

• Estimation: Point estimates and confidence intervals for population parameters.

• Hypothesis Testing: Procedures for testing claims about population parameters.

• Types of Errors: Type I (false positive) and Type II (false negative).

• Example: Testing whether a new drug is more effective than the current standard.

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

• Hypothesis Test Steps:

  1. State null and alternative hypotheses.

  2. Choose significance level ($\alpha$).

  3. Calculate test statistic.

  4. Find p-value and make a decision.

6. Statistical Reasoning and Applications

Statistical reasoning involves interpreting data, drawing conclusions, and making informed decisions based on evidence.

• Critical Thinking: Evaluating sources of bias, reliability, and validity of data.

• Applications: Social sciences, psychology, health sciences, business, and more.

• Example: Using statistical analysis to determine the effectiveness of a public health intervention.

Course Objectives & Exit Skills

• Summarize and interpret data.

• Identify methods of obtaining data and their advantages/disadvantages.

• Analyze graphical presentations of data.

• Find and interpret measures of central tendency and dispersion.

• Analyze and interpret probability distributions.

• Distinguish between sample and population distributions.

• Apply the Central Limit Theorem.

• Formulate and test hypotheses.

• Interpret confidence intervals and p-values.

• Use statistical software and calculators for analysis.

Grading Policy

• Stat C1000: Weighted average of quizzes, exams, participation, and discussion.

• Formula for UTS (Total Score): $\text{UTS} = 20\% \times \text{UQ} + 5\% \times \text{UH} + 5\% \times \text{UPT} + 42\% \times \text{UTE} + 28\% \times \text{UTF}$

• Math 54C: Pass/No Pass based on completion of Stat C1000 with a grade of C or higher.

Sample HTML Table: Tentative Schedule

The following table summarizes the tentative schedule for the first weeks of the course, including topics and suggested homework assignments.

Day	Sections & Suggested Homework
9/2	Introduction to the Practice of Statistics, Syllabus, Random Sampling, Designed Experiments
9/4	Simple Random Sample, Sampling Methods, The Design of Experiments
9/9	Organizing Qualitative Data, Quantitative Data, Misrepresentations of Data
9/11	Real Numbers, Operations, Inequalities, Percents, Fractions, Decimals
9/16	Measures of Central Tendency, Measures of Variation, Measures of Position
9/23	Measures of Central Tendency, Dispersion for Grouped Data, Measures of Position and Outliers

Student Learning Outcomes

• Apply knowledge of access skills and academic behaviors to support success in statistics.

• Collect, organize, and analyze mathematical models and graphs.

• Communicate mathematical reasoning effectively.

Additional Info

• Emergency preparedness, campus emotional support, Title IX, and accessibility resources are available to all students.

• Attendance and withdrawal policies are outlined in the syllabus.

• Academic integrity is strictly enforced; violations may result in disciplinary action.