Elementary Statistics I – Course Syllabus and Study Guide

Course Overview

This course, Elementary Statistics I, provides an introduction to statistics for students without a calculus background. It covers foundational concepts in data analysis, probability, statistical estimation, and hypothesis testing, with a focus on practical applications and interpretation of results. The course is structured to develop statistical reasoning and data literacy, preparing students for further study or application in various fields.

Course Topics and Structure

• Introduction to Statistics (Textbook Sections 1.1 - 1.4)

• Exploring Data with Tables and Graphs (Sections 2.1 - 2.4)

• Describing, Exploring, and Comparing Data (Sections 3.1 - 3.3)

• Probability (Sections 4.1 - 4.3)

• Discrete Probability Distributions (Sections 5.1 - 5.3)

• Normal Probability Distributions (Sections 6.1 - 6.3)

• Central Limit Theorem and Determining Normality (Sections 6.3 - 6.5)

• Estimation and Determining Sample Sizes for the Population Mean (Section 7.2)

• Hypothesis Testing for the Population Mean (Section 8.3)

• Estimation, Hypothesis Testing, and Determining Sample Sizes for the Population Proportion (Sections 7.1 and 8.2)

Course Learning Outcomes

• Produce appropriate numerical, graphical, and tabular summaries of data to investigate and describe distributions and relationships between variables.

• Correctly interpret correlation and distinguish between observational and experimental studies.

• Compute probabilities using discrete probability models and random variables; demonstrate understanding of independence.

• Use the Normal distribution to compute probabilities and make statements about sample means and proportions (Central Limit Theorem).

• Estimate population parameters using point estimates and confidence intervals; interpret confidence intervals, margin of error, and confidence level.

• Formulate statistical hypotheses, describe the logic of hypothesis testing, and use p-values or statistical significance to draw conclusions.

Assessment and Grading Policy

The course uses a combination of practice sets, quizzes, Excel projects, participation, and unit assessments to evaluate student understanding. The grading breakdown is as follows:

Grading Category	Percentage
Practice Set Average	15%
Quiz Average	15%
Excel Project Average	15%
Participation	5%
Units 1-5 Assessment	25%
Units 6-10 Assessment	25%

Grades are assigned according to the following scale:

Percentage	Grade
93.0 - 100.0	A
90.0 - 92.9	A-
87.0 - 89.9	B+
83.0 - 86.9	B
80.0 - 82.9	B-
77.0 - 79.9	C+
73.0 - 76.9	C
70.0 - 72.9	C-
< 70.0	NP, F, X, or UW

Key Course Policies

• Practice Sets, Quizzes, and Excel Projects: Unlimited attempts before due date; lowest score dropped at semester end.

• Participation: Based on attendance or review assignments; see syllabus for details.

• Unit Assessments: In-person, proctored; makeup/retake opportunities available with documentation.

• Late Assignments: 6-day grace period for non-assessment assignments; no further extensions.

• Academic Integrity: Use of AI tools is prohibited; all work must be original.

Course Calendar (Selected Weeks)

Week/Module	Topic	Assignments	Due Date
1	Introduction to Statistics	Survey #1, Practice Set #1, Quiz #1	Friday Aug 28
2	Exploring Data with Tables and Graphs	Survey #2, Practice Set #2, Quiz #2	Friday Sept 4
3	Describing, Exploring, and Comparing Data	Survey #3, Practice Set #3, Quiz #3	Friday Sept 11
4	Probability	Survey #4, Practice Set #4, Quiz #4	Friday Sept 18
5	Discrete Probability Distributions	Survey #5, Practice Set #5, Quiz #5	Friday Sept 25
6	Normal Probability Distributions	Survey #6, Practice Set #6, Quiz #6	Friday Oct 16
7	Central Limit Theorem and Determining Normality	Survey #7, Practice Set #7, Quiz #7	Friday Oct 23
8	Estimation and Determining Sample Sizes for the Population Mean	Survey #8, Practice Set #8, Quiz #8	Friday Oct 30
9	Hypothesis Testing for the Population Mean	Survey #9, Practice Set #9, Quiz #9	Friday Nov 6
10	Estimation, Hypothesis Testing, and Determining Sample Sizes for the Population Proportion	Survey #10, Practice Set #10, Quiz #10	Friday Nov 13

Additional Resources and Policies

• Accessibility: Students with disabilities are encouraged to register with UC Accessibility Resources for accommodations.

• Academic Support: The Learning Commons offers tutoring, coaching, and writing support.

• Attendance: Regular attendance is expected; see syllabus for details on excused absences and participation grading.

• Technology: Use only course-related technology during class; personal devices are not permitted during assessments.

• Communication: Use university email for all course-related communication; expect responses within 48 hours on weekdays.

Course Materials

• Textbook: Elementary Statistics using Excel, 7th Edition (Pearson, included with registration)

• Calculator: TI 83/84 graphing calculator or other scientific calculator (optional)

Major Topics Covered (with Academic Context)

Introduction to Statistics

Statistics is the science of collecting, analyzing, interpreting, and presenting data. It provides tools for making informed decisions in the presence of uncertainty. Key concepts include populations, samples, variables, and types of data (categorical vs. numerical).

• Population: The entire group of individuals or items of interest.

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

• Variable: A characteristic or property that can take on different values.

Describing Data with Tables and Graphs

Data can be summarized and visualized using tables and graphical displays. Common methods include frequency tables, histograms, bar charts, and pie charts. These tools help reveal patterns, trends, and outliers in the data.

• Frequency Table: Summarizes data by showing the number of observations in each category or interval.

• Histogram: A graphical representation of the distribution of numerical data.

• Bar Chart: Used for categorical data to compare frequencies or proportions.

Describing Data Numerically

Numerical summaries provide measures of central tendency (mean, median, mode) and variability (range, variance, standard deviation). These statistics describe the center and spread of the data.

• Mean: The arithmetic average of a set of values.

• Median: The middle value when data are ordered.

• Standard Deviation: Measures the average distance of data points from the mean.

Key formulas:

• Sample mean: $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

• Sample standard deviation: $s = \sqrt{ \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 }$

Probability

Probability quantifies the likelihood of events occurring. It is foundational for statistical inference. Key rules include the addition and multiplication rules, and the concept of independent events.

• Probability of an event: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Independent events: Two events are independent if the occurrence of one does not affect the probability of the other.

Discrete and Normal Probability Distributions

Probability distributions describe how probabilities are distributed over values of a random variable. Discrete distributions (e.g., binomial) apply to countable outcomes, while the normal distribution is continuous and bell-shaped.

• Binomial Distribution: $P(X = k) = {n \choose k} p^k (1-p)^{n-k}$

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

Central Limit Theorem (CLT)

The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution, provided the samples are independent and identically distributed.

• Sampling distribution mean: $\mu_{\bar{x}} = \mu$

• Sampling distribution standard deviation (standard error): $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

Estimation and Confidence Intervals

Confidence intervals provide a range of plausible values for a population parameter, based on sample data. The margin of error reflects the precision of the estimate.

• Confidence interval for mean (known $\sigma$): $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

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

Hypothesis Testing

Hypothesis testing is a formal procedure for comparing observed data to a claim about a population. It involves stating null and alternative hypotheses, calculating a test statistic, and using the p-value to make a decision.

• Null hypothesis ($H_0$): The default assumption (e.g., no effect or difference).

• Alternative hypothesis ($H_a$): The claim to be tested.

• Test statistic for mean: $z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$

• p-value: The probability of observing data as extreme as, or more extreme than, the observed value under $H_0$.

Using Excel for Statistics

Excel is used throughout the course for data analysis, including creating graphs, calculating descriptive statistics, and performing hypothesis tests. Students complete projects analyzing real-life data sets using Excel tools.

Support and Resources

• Learning Commons: Tutoring, coaching, and writing support available.

• Accessibility Resources: Accommodations for students with disabilities.

• Mental Health and Safety: Counseling, public safety, and resource centers are available for student support.

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