Pecan Campus · Math, Science & IT · Mathematics
Elementary Statistical Methods
MATH-1442
1-Full Term(Spring) 2023 Section P03 4 Credits 01/17/2023 to 05/11/2023 Modified 01/17/2023
 Meeting Times
Campus:PCN Bldg:PCNY Room:2-103 Day:TR Time:10:00AM - 11:45AM
 Course Description
This course is a presentation and interpretation of data, probability, sampling, correlation and regression, analysis of variance, and use
of statistical software. Prerequisite: Meet TSI college-readiness standard for Mathematics; or completion of MATH 0200 or MATL
0020 or MATH 0442 or MATL 0014 or MATL 0024 with a grade of "P" or "C" or better; or completion of or concurrent enrollment in
MATL 0042 with a grade of "C" or "P" or better; or equivalent.
 Contact Information
Instructor Name: Daniel Montez
Office Location: Pecan J 2.804B
Telephone #: 956-872-6771 The best way to contact me is through Pronto or e-mail (below)
Email: dmontez_1994@southtexascollege.edu
Office Hours:
MW (Online: Teams/Pronto/Bb Messages): 12:20 pm - 1:20 PM
TR: 12:00 pm - 1:00 pm
F(Online: Teams/Pronto/Bb Messages) 10:00 am-11:00 am
Department Web Page: https://ms.southtexascollege.edu/math/index.html
 Program Learning Outcomes
Demonstrate in-depth knowledge of Mathematics, its scope, application, history, problems, methods, and usefulness to mankind
both as a science and as an intellectual discipline.
Demonstrate a sound conceptual understanding of Mathematics through the construction of mathematically rigorous and
logically correct proofs.
Identify, formulate, and analyze real world problems with statistical or mathematical techniques.
Utilize technology as an effective tool in investigating, understanding, and applying mathematics.
Communicate mathematics effectively to mathematical and non-mathematical audiences in oral, written, and multi-media form.
 Course Learning Outcomes
Explain the use of data collection and statistics as tools to reach reasonable conclusions.
Recognize, examine and interpret the basic principles of describing and presenting data.
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Compute and interpret empirical and theoretical probabilities using the rules of probabilities and combinatorics.
Explain the role of probability in statistics.
Examine, analyze and compare various sampling distributions for both discrete and continuous random variables.
Describe and compute confidence intervals.
Solve linear regression and correlation problems.
Perform hypothesis testing using statistical methods.
 Required Core Objectives
CRITICAL THINKING SKILLS: to include creative thinking, innovation, inquiry, and analysis, evaluation and synthesis of
information.
COMMUNICATION SKILLS: to include effective development, interpretation and expression of ideas through written, oral and
visual communication.
EMPIRICAL AND QUANTITATIVE SKILLS: to include the manipulation and analysis of numerical data or observable facts
resulting in informed conclusions.
 Core Objectives Matrix
Assessment
Required Core
Objectives
(Department or faculty
determined)
(three to four per
component area)
Applied to
(Remove those that do
Examples: Essays / multiple
choice / discussion session /
short answer /common
(Course appropriate
topic-Department or
not apply to the course) faculty determined)
Passing Standard
Target: Expected % of Students
Meeting Core Objective
(College-wide approved)
(College wide approved)
Approved passing standard on
Institutional Rubric
70%
assessment exam
EMPIRICAL AND
QUANTITATIVE SKILLS
 Course Requirements
Grading Criteria
Letter Grade A
Range
B
C
D
F
100-90% 89-80% 79-70% 69-60% 59-0%
Breakdown
Evaluation Method
Homework (Study Plan): 20%
Quizzes: 25%
Exams/Assessments/Final Exam (All Proctored In-Class): 45%
Presentation: 10%
Departmental Course Requirements:
All exams are closed-book proctored exams! also. The instructor will determine if make-ups are allowed.
Exam results will be given within one (1) week from the exam day.
Check with the instructor on the usage of cell phones, cell phone calculators, iPod, or electronics during exams.
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Check with the instructor for the type of calculator allowed (4-function, scientific, graphing, other), if any.
Addendum Faculty expectations:
 Textbooks & Resources
Exemplar Statistics Alpha Book
The textbook is provided at no cost.
 Instructor Expectations
 Topic Outline
Module 1: Data Types and Organization
1.0
1.1
Review topics needed for success in Data Types and Organization
1.0.1
Write a proportion from a table.
1.0.2
Use proportions to answer questions.
1.0.3
Simplify fractions by removing common factors.
1.0.4
Convert between fractions and decimals
1.0.5
Identify statistical questions
Thinking Statistically
1.1.1
1.2
1.3
Understand the statistical investigative process
Inclusive Learning Community and Belonging
1.2.1
Building an inclusive learning community within the classroom OR Building a supportive classroom
environment
1.2.2
Helping students establish academic belonging
Data Collection and Organization
1.3.1
Identify statistical investigative questions and survey questions.
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1.4
1.3.2
Identify the subjects, cases, and observational units in a statistical study.
1.3.3
Identify and classify variables by their characteristics.
Statistical Questions
1.4.1
1.5
Design good statistical questions for a given set of data.
Cooperative and Collaborative Learning
1.5.1
Develop effective and inclusive teamwork and communication skills
1.5.2
Engaging students through cooperative and collaborative learning
Module 2: Statistical Studies and Sampling
2.0
2.1
Review topics needed for success in Statistical Studies and Sampling
2.0.1
Use technology to create a dotplot from a dataset.
2.0.2
Answer questions about a variable using a dotplot.
2.0.3
Use a random number generator to select a random sample.
2.0.4
Calculate sample mean by hand.
2.05
Apply a statistical definition to the word random.
2.06
Distinguish between a population and a sample.
2.07
Distinguish between a parameter and a statistics.
2.08
Identify explanatory and response variables in a scenario.
2.09
Ceate a table to record data on explanatory/response variables.
2.10
Identify whether a variable is categorical or quantitative.
Random Sampling
2.1.1
Describe and determine the population, sample, parameter, and statistic of the study
2.1.2
Select a simple random sample from a finite population using a random number generator to estimate a
population proportion.
2.1.3
2.2
2.3
Determine and explain bias in a sampling method
Sampling Methods
2.2.1
Understand and apply different sampling methods
2.2.2
Use a representative sample from a population to make inferences about the population
Experimental Design
2.3.1
Identify key components of experimental design, including: treatment, factor of interest (also known as
the explanatory variable or independent variable), response variable (also known as the dependent
variable), nuisance factors, random assignment, and replication.
2.3.2
Design a hypothetical experiment to answer a research question.
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2.4
2.5
Observational Studies
2.4.1
Identify an observational study.
2.4.2
Identify possible confounding factors that might explain an apparent association.
Advanced Experimental Design
2.5.1
Describe how to use a completely randomized block design for a given research objective.
2.5.2
Determine whether or not an experiment has been designed well.
Module 3: Describing Data Graphically
3.0
3.1
3.2
3.3
3.4
Review topics needed for success in Describing Data Graphically
3.0.1
Round decimals to a specified place value
3.0.2
Convert fractions or mixed numbers to decimals
3.0.3
Convert decimals and fractions to percents
3.0.4
Find the unknown in a percent problem
3.0.5
Calculate absolute and relative change between two values
3.0.6
Write and solve percent proportion equations
Displaying Categorical Data
3.1.1
Construct pie charts and bar graphs to display data by hand and with technology
3.1.2
Use the displayed data distribution of categorical data to answer research questions
Applications of Bar Graphs
3.2.1
Identify the differences between side-by-side and stacked bar graphs
3.2.2
Construct side-by-side and stacked bar graphs using technology
3.2.3
Read and interpret side-by-side and stacked bar graphs to compare different groups
Visualizing Quantitative Data
3.3.1
Identify and construct the most useful graphical display(s) to answer a given research question
3.3.2
Compare and contrast features present in different graphical displays of quantitative data
Distribution of Quantitative Variables
3.4.1
3.5
Summarize the description of a distribution of a quantitative variable using the shape, center, spread, and
presence of outliers
Comparing Quantitative Distributions
3.5.1
Compare shape, center and spread of distributions across groups
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Module 4: Describing Data Numerically
4.0
4.1
4.2
4.3
4.4
4.5
Review topics needed for success in Describing Data Numerically
4.0.1
Read and interpret a dot plot
4.0.2
Read and interpret a histogram
4.0.3
Understand the difference between mean and median
4.0.4
Evaluate expressions that contain absolute value
4.0.5
Calculate the median of a dataset by hand
4.0.6
Calculate the mean of a dataset by hand
Measures of Center
4.1.1
Identify and compare measures of center for data presented in a graph
4.1.2
Calculate and use measures of center to make statistical inference
Interpretation of Mean and Median
4.2.1
Identify distribution characteristics of a data set
4.2.2
Analyze the relationship between data set distribution, mean and median
Boxplot Data and Displays
4.3.1
Use boxplots to draw inferences
4.3.2
Interpret features of boxplot (5-number summary) and use it to identify the upper and lower outliers.
4.3.3
Use boxplots to compare the distributions of multiple populations
Measures of Variability
4.4.1
Identify and compare measures of variability for data presented in a graph
4.4.2
Calculate and use measures of variability to make statistical inference
Z-Score and the Empirical Rule
4.5.1
Utilize standardized scores and the Empirical Rule to analyze observed values
4.5.2
Compare two observations by calculating and comparing z-scores
Module 5: Displaying and Describing Bivariate Data
5.0
Review topics needed for success in Displaying and Describing Bivariate Data
5.0.1
Identify the two quantitative variables as an explanatory variable and a response variable.
5.0.2
Understand what a dot in a scatterplot represents.
5.0.3
Reading and interpreting heat maps.
5.0.4
Calculate a change in percentage.
5.0.5
Calculate relative frequency.
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5.1
5.2
5.0.6
Recognize when a graph includes a misleading scale.
5.0.7
Recognize when a graph includes a missing component.
5.0.8
Recognize the importance of appropriate color in a graph.
Scatterplot
5.1.1
Create and interpret effective graphical display for bivariate data.
5.1.2
Describe the trend of a bivariate data.
5.1.3
Identify linear relationships, non-linear relationships, and outliers.
5.1.4
Calculate and interpret the Pearson Correlation Coefficient between two quantitative variables.
Complex Graphical Displays
5.2.1
5.3
Read and interpret different components of complex graphical displays
Effective Visualizations
5.3.1
Demonstrate how to use a rating scale and best practices criteria to think critically about graphical
displays.
Module 6: Modeling Bivariate Data
6.0
Review topics needed for success in Modeling Bivariate Data
6.0.1
Identify the independent and dependent variables of a given scenario.
6.0.2
Recognize linear patterns from a given context
6.0.3
Choose appropriate axes labels for a given scenario
6.0.4
Interpret an ordered pair (x, y) that represents a data point on a graph.
6.0.5
Use the graph of a linear trend to make predictions
6.0.6
Write a linear equation to describe a given scenario.
6.0.7
Identify and interpret the slope and y-interecept of a linear model
6.0.8
Calculate the slope using [latex]\dfrac{\text{rise}}{\text{run}}.
6.0.11 Identify the slope and y-intercept given the graph of a line.
6.0.12 Sketch the graph of a line given its y-intercept and slope.
6.0.13 Compare and contrast correlation coefficients among different scatterplots
6.0.19 Calculate and interpret residual errors.
6.0.20 Use technology to calculate a line of best fit.
6.1
Line of Best Fit
6.1.1
Identify the explanatory and response variables given the context of the study.
6.1.2
Understand the concept of the least square regression analysis and the line best fit.
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6.1.3
Identify when a linear regression analysis might be appropriate and use technology to perform the least
squares regression analysis.
6.1.4
6.2
Calculate and draw the equation of the line of best fit and the correlation coefficient [latex]r[/latex].
Equation of the Line of Best Fit
6.2.1
Identify and interpret the estimated slope and estimated y-intercept given the equation of the line best fit
in the context of a problem.
6.2.2
6.3
Assess the model accuracy and fit and make appropriate predictions/extrapolations.
Coefficient of Determination
6.3.1
Understand the relationship between the sign of the slope, the spread and shape of the data, and the
coefficient of determination [latex]R^2[/latex].
6.3.2
Identify and interpret the meaning of [latex]R^2[/latex] in context of a problem and determine its utility in
different tasks (gauging prediction strength vs. determining a causal relationship).
6.4
6.5
Assessing the Fit of a Line
6.4.1
Determine the relationship between the residual and the proximity and location of a particular data point
to the line of best fit.
6.4.2
Construct and interpret a residual plot and identify influential points to assess the appropriateness of the
linear regression model.
Making Predictions
6.5.1
Use the line of best fit to predict the value of the response variable for a given value of the explanatory
variable.
6.5.2
Calculate residuals and standard error of the residuals to assess the reliability of the predictions.
Module 7: Probability
7.0
7.1
Review topics needed for success in Probability
7.0.1
Identify possible outcomes of a chance experiment.
7.0.2
Calculate probabilities of “equally likely” outcomes.
7.0.3
Using simulations to estimate probabilities of events.
7.0.4
Build contingency (two-way) table.
7.0.5
Describe cells in a two-way tables.
7.0.6
Use contingency tables to calculate probabilities.
7.0.7
Use contingency tables to calculate conditional probabilities.
7.0.8
Create contingency tables based on word problems.
7.0.9
Calculate conditional probability using a contingency table.
Probability
7.1.1
Determine the empirical probability of an event in a chance experiment
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7.1.2
7.2
7.3
7.4
Understand the difference between theoretical and empirical probabilities
Probabilities of Two Events
7.2.1
Find and interpret the probability of compound events using unions, intersections, and complements
7.2.2
Find the probability of one event AND/OR/and NOT another event.
Conditional Probabilities
7.3.1
Calculate and interpret conditional probabilities
7.3.2
Describe the condition for mutually exclusive and independent events using probabilities
More Conditional Probabilities
7.4.1
Create contingency tables and calculate conditional probabilities
Module 8: Probability Distributions
8.0
Review topics needed for success in Probability Distributions
8.0.1
Construct a probability distribution table.
8.0.2
Construct a probability distribution table using a simulation.
8.0.3
Compute probabilities that involve exponents.
8.0.4
Interpret statements of inequality.
8.0.5
Label the means and standard deviations of histograms.
8.0.6
Calculate the values that are ±1, ±2, and ±3 standard deviations from the mean.
8.0.7
Know where those values are on a histogram.
8.0.8
Describe the position of a data value in a normal distribution.
8.0.9
Relate the Empirical Rule and the standard normal curve.
8.0.10 Use the Empirical Rule to calculate percentages and probabilities.
8.1
8.2
8.3
8.4
Probability Distributions
8.1.1
Construct and interpret a probability model to determine the likelihood of an outcome
8.1.2
Recognize discrete and continuous probability distributions
Discrete Probability Distributions
8.2.1
Construct and analyze a discrete probability distribution for a random variable
8.2.2
Interpret a discrete probability distribution to calculate probabilities
Binomial Distributions
8.3.1
Apply a binomial distribution to real-world questions
8.3.2
Explain the conditions of a binomial distribution
Normal Distributions
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8.5
8.6
8.4.1
Construct and interpret a normal distribution using mean and standard deviation
8.4.2
Understand how mean and standard deviation affects the shape and spread of a normal distribution
curve
8.4.3
Estimate percentages and values using normal curves
Normal Distributions (Continued)
8.5.1
Calculate percentiles and probabilities for a normal distribution
8.5.2
Describe the standard normal curve and interpret the meaning of a z-score
Connection between Binomial and Normal Distributions
8.6.1
Approximate binomial probabilities using a normal distribution
8.6.2
Determine when a normal distribution can be used to approximate a binomial distribution
Module 9: Introduction to Sampling Distributions
9.0
9.1
9.2
9.3
Review topics needed for success in Data Types and Organizations
9.0.1
Write a proportion in fraction form from a table.
9.0.2
Use proportions to answer questions.
9.0.3
Simplify fractions by removing common factors.
9.0.4
Convert between fractions and decimals
Inference Basics
9.1.1
Identify the population and sample of interest and their characteristics.
9.1.2
Describe the parameter of interest and compute the appropriate sample statistics in context of the
problem.
Sampling distribution of a sample proportion
9.2.1
Construct a sampling distribution of a sample proportion for a given sample size and population
proportion.
9.2.2
Calculate the mean and standard deviation for the sampling distribution of a sample proportion.
9.2.3
Understand the difference between the standard deviation and the standard error of a sample proportion.
Sampling Variability
9.3.1
Determine the required sample size for a given standard deviation of sample proportions in a sampling
distribution.
9.3.2
Determine whether the normal approximation is valid for the sampling distribution of a sample proportion
based on the sample size and population proportion.
9.3.3
Use the normal distribution to approximate probabilities and percentiles involving sample proportions.
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Module 10: Confidence Intervals for Population Proportions
10.0 Review topics needed for success in Data Types and Organizations
10.1 Confidence intervals for proportions
10.1.1 Determine if the conditions for creating confidence intervals for a proportion are met.
Construct a confidence interval for a population proportion
10.1.2 Understand the relationship between confidence level and the confidence interval.
10.2 Confidence intervals for proportions (continued)
10.2.1 Construct and interpret confidence intervals for population proportions when conditions are met.
10.2.2 Identify common misinterpretations associated with confidence intervals.
10.3 Sample size for proportions
10.3.1 Determine the sample size needed to achieve a given margin of error when working with proportions.
10.4 Confidence Intervals for the Difference in Population Proportions
10.4.1 Calculate a confidence interval for the difference in proportions between two groups.
10.4.2 Use confidence intervals to draw conclusions about an analysis question.
Module 11: Hypothesis Testing for Population Proportions
11.0 Review topics needed for success in Data Types and Organizations
11.1 Null and alternative hypotheses
11.1.1 Construct null and alternative hypotheses for a hypothesis test.
11.1.2 Identify in context whether sample statistics would serve as evidence against a null hypothesis.
11.2 Test statistics
11.2.1 Calculate a test statistic and interpret its value in context.
11.2.2 Use a test statistic to decide whether the null hypothesis about a population proportion is a plausible
explanation for sample results.
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11.3 P-value
11.3.1 Use a P-value to make a decision about a null hypothesis.
11.3.2 Calculate and identify a P-value.
11.4 One-sample Hypothesis test for proportions
11.4.1 Conduct a one-sample z-test for proportions that includes conclusions.
11.4.2 Use the P-value to support the conclusions of a complete hypothesis test.
11.5 Errors in Hypothesis Testing
11.5.1 Identify Type II and Type II errors and explain the implications of each in context.
11.5.2 Determine whether results have statistical and practical significance.
11.6 Two sample test for proportions
11.6.1 Conduct a two-sample z-test of proportions and interpret the results in context.
11.6.2 Distinguish between situations that require a one-sample test of proportions or a two-sample test of
proportions.
11.7 Connecting Tests & Intervals
11.7.1 Describe the connections between confidence intervals and two-sided hypothesis tests
Module 12: Confidence Intervals for Population Means
12.0 Review topics needed for success in Data Types and Organizations
12.0.1 Write a proportion in fraction form from a table.
12.0.2 Use proportions to answer questions.
12.0.3 Simplify fractions by removing common factors.
12.0.4 Convert between fractions and decimals
12.1 Sampling distribution of a sample mean
12.1.1 Construct a sampling distribution of a sample mean for a given sample size and population mean.
12.1.2 Calculate the mean and standard deviation for the sampling distribution of a sample mean.
12.1.3 Determine when the Central Limit Theorem can be applied to means.
12.1.4 Use the normal approximation to compute probabilities involving sample means.
12.2 t-distribution
12.2.1 t-distribution: understand, model, calculate, assess, and finding probabilities.
12.3 Confidence Interval for a Population Mean
12.3.1 Assess whether the assumptions for a one-sample t confidence interval to estimate a population mean
are reasonably met.
12.3.2 Calculate and interpret a confidence interval for a population mean.
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12.4 Confidence Interval for Difference in Population Means
12.4.1 Assess whether the assumptions for a two-sample t confidence interval to estimate a difference in
population means are reasonably met.
12.4.2 Calculate and interpret a confidence interval for population means.
Module 13: Hypothesis Testing for Population Means
13.0 Review topics needed for success in Data Types and Organizations
13.1 Null and alternative hypothesis for means
13.1.1 Recognize when and why statistical test are needed.
13.1.2 Identify and write the null and alternative hypothesis in the context of means for one-sample tests and
two-sample tests.
13.1.3 Identify whether assumptions for a hypothesis test for means have been met.
13.2 One Sample Hypothesis Test for Means
13.2.1 Perform and interpret the results of a hypothesis test about one population mean in context.
13.2.2 Connect the results of the hypothesis test to a confidence interval
13.3 Comparing Two Population Means (Independent Samples)
13.3.1 Perform and interpret the results of a hypothesis test comparing two (independent) population means in
context.
13.3.2 Connect the results of the hypothesis test to a confidence interval
13.4 Comparing Two Population Means (Dependent Samples)
13.4.1 Perform and interpret the results of a hypothesis test for the difference between two population means
with a dependent sample.
13.4.2 Build a connection between confidence intervals and hypothesis tests for the difference between two
population means with a dependent sample.
 Additional Items
Student Attendance Guidelines “Student Attendance Board Policy 3335”
Class attendance and participation are essential to student success. Regular and punctual class attendance is expected at South
Texas College. Student absences will be recorded from the first day the class meets. It is imperative that students attend on the first
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day of class. This is when the course syllabus, schedule, deadlines, and class expectations will be discussed. In case of absence, it is
the student's responsibility to contact the instructor prior to the absence. The student is expressly responsible for any work missed
regardless of the cause of the absence. The student must discuss such work with the instructor and should do so immediately on
returning to school. Communication between the student and faculty member is most important, and it is the student's responsibility
to initiate such communication. The faculty member will determine, based on policies outlined in the course syllabus, whether the
student will be permitted to make up work and will decide on the time and nature of the makeup. If a student does not appear at the
prearranged time or meet the prescribed deadline for makeup work, they forfeit their rights for further makeup of that work. A student
who stops attending class for any reason should contact the faculty member and the Admission’s office to officially withdraw from
the class. Failure to officially withdraw may result in a failing grade for the course.
Syllabus Disclaimer
Information contained in this syllabus is, to the best knowledge of this Instructor, considered correct and complete when
distributed to the student. The Instructor reserves the right, acting within policies and procedures of South Texas College, to make
necessary changes in course content or instructional techniques without prior notice or obligation to the student. Any changes
made would be communicated accordingly.
Calendar
Calendar
Week 1
Module 1
Study Plan and Quiz
Week 2
Module 1
Study Plan and Quiz
Week 3
Module 2
Study Plan and Quiz
Week 4
Module 3
Study Plan and Quiz
Week 5
Module 4
Study Plan and Quiz
Week 6
Module 5
Study Plan, Quiz, and Exam 1
Week 7
Module 6
Study Plan and Quiz
Week 8
Module 7
Study Plan and Quiz
Week 9
Module 8
Study Plan and Quiz
Week 10
Module 9
Study Plan and Quiz
Week 11
Module 10
Study Plan, Quiz and Exam 2
Week 12
Module 11
Study Plan and Quiz
Week 13
Module 12
Study Plan and Quiz
Week 14
Module 13
Study Plan and Quiz
Week 15
Module 13
Study Plan and Quiz
Week 16
Module 14
Final Exam
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