Department of Mathematics, Kent State University
(Draft) MATH 10041 INTRODUCTORY STATISTICS
Version x.x Date YYYY-MMM-DD
Content:
Kent Core Learning Objectives ............................................................................................................................................................. 1
(Ohio Transfer Module) Acquire critical thinking and problem solving skills .................................................................................. 1
(Ohio Transfer Module) Apply principles of effective written and oral communication ................................................................ 5
A Broaden their imagination and develop their creativity .............................................................................................................. 5
Cultivate their natural curiosity and begin a lifelong pursuit of knowledge ................................................................................... 5
Develop competencies and values vital to responsible uses of information and technology op competencies and values vital to
responsible uses of information and technology ............................................................................................................................ 5
(Ohio Transfer Module) Engage in independent thinking, develop their own voice and vision, and become informed,
responsible citizens ......................................................................................................................................................................... 5
(Ohio Transfer Module) Improve their understanding of issues and behaviors concerning inclusion, community and tolerance 5
Increase their awareness of ethical implications of their own and others’ actions ........................................................................ 5
Integrate their major studies into the broader context of a liberal education ............................................................................... 5
Strengthen quantitative reasoning skills ......................................................................................................................................... 5
(Ohio Transfer Module) Understand basic concepts of the academic discipline ........................................................................... 6
Examples of Detailed Learning Outcomes with Assessment Rubrics ................................................................................................... 6
Kent Core Learning Objectives
(Ohio Transfer Module) Acquire critical thinking and problem solving skills
About the data (reference Chapter 1, section 1.1 and 1.2 from the current text)
a.
b.
c.
d.
Explain the meaning of the word “statistics.”
Distinguish between a variable in algebra and a variable in statistics.
Distinguish between numerical and categorical variables.
Understand methods for coding categorical variables
Categorical Data (reference Chapter 1, sections 1.3 and 1.4 from the current text)
a. Know how to find and use rates (including percentages) and understand when and why they are more useful
than counts for describing and comparing groups.
b. Understand when it is possible to infer a cause-and-effect relationship.
c. Explain how confounding variables prevent us from inferring causation, and suggest confounding variables
that are likely to occur in some situations.
d. Be able to distinguish between observational studies and controlled experiments.
Graphical Data Representation (reference Chapter 2, sections 2.1 and 2.2 from the current text)
a. Understand that a distribution of a sample of data displays a variable’s values and the frequencies (or relative
frequencies) of those values.
b. Know how to make graphs of distributions of numerical variables and how to interpret the graphs in context.
c. Be able to compare centers and spreads of distributions of samples informally.
Visualizing Categorical Data (reference Chapter 2, sections 2.3,v2.4, and 2.5 from the current text)
a. Understand that a distribution of a sample of data displays a variable’s values and the frequencies (or relative
frequencies) of those values.
MATH 10041 INTRODUCTORY STATISTICS
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Department of Mathematics, Kent State University
b. Know how to make graphs of distributions of categorical variables and how to interpret the graphs in
context.
c. Be able to compare centers and spreads of distributions of samples informally.
Analysis of Symmetrical Distributions (reference Chapter 3, section 3.1 from the current text)
a.
b.
c.
d.
e.
f.
Explain what the mean of a data set is
Interpret the mean in context
Approximate the mean given a histogram
Find the mean of a data set using the formula
Explain what the standard deviation is and interpret it in context
Given the mean and the standard deviation of a data set, find the values that are one standard deviation
above or below the mean
g. Calculate the standard deviation of a small data set given the formula
h. Explain why the standard deviation is a reasonable measure of variation
i. Given histograms of several data sets, determine data set has the largest standard deviation
The Empirical Rule and z-scores (reference Chapter 3, section 3.2 from the current text)
a. Be able to state the Empirical Rule
b. Given a histogram, locate approximate boundary points within one, two, or there standard deviations of the
mean
c. Given a mean and standard deviation of a data set, use the Empirical Rule to decide if a given data point is
unusual for that data set
d. Explain what a z-score is and be able to calculate and interpret z-scores in context
Skewed Distributions (reference Chapter 3, section 3.3 from the current text)
a.
b.
c.
d.
Explain what the mean of a data set is and how to find it
Find quartiles 1-3 and interquartile range
Determine the effect of outliers to median and mean.
Be able to correctly identify measures of center and spread when comparing two distributions.
Measures of center and Boxplots (reference Chapter 3, sections 3.4 and 3.5 from the current text)
a. Be able to write comparisons between samples of data in context
b. Be able to interpret boxplots
c. Be able to compare boxplots to histograms
Scatterplots (reference Chapter 4, section 4.1 from the current text)
a. Look at the associated scatterplot of the variables and learn as much as you can about the association.
b. Examine the trend, strength, and shape. Identity any possible outliers.
c. Be able to write a clear description of the association between the two variables.
Correlation Coefficient (reference Chapter 4, section 4.2 from the current text)
a. Be able to approximate with reasonable accuracy the numerical value of the correlation coefficient by a
visual inspection of the scatterplot.
b. Be able to calculate the exact value of the correlation coefficient using appropriate technology.
Modeling Linear Trends (reference Chapter 4, section 4.3 from the current text)
a. Understand how to use a regression line to summarize a linear association between two numerical variables.
b. Know how to differentiate between the explanatory and response variable, order matters when choosing
which variable to represent “x” and “y”.
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Department of Mathematics, Kent State University
c. Be able to interpret the slope and the intercept of the regression line.
d. Know how to use the regression line to predict the mean value of the response variable .
Evaluating the Linear Model (reference Chapter 4, section 4.4 from the current text)
a. Be able to determine how “good” is the best fit line by using coefficient of determination.
b. Be able to critically evaluate a regression model:
- Don’t extrapolate
- Don’t make cause-and-effect conclusions if the data are observational
- Beware of outliers, which may or may not strongly affect the regression line
- Proceed with caution when dealing with aggregated data
Random Experiments, Sample Spaces and Probabilities (reference Chapter 5, section 5.1 from the current text)
a. Understand that humans can’t reliably create random numbers or sequences.
b. Understand that probability is a long-term relative frequency.
c. Know the difference between empirical and theoretical probabilities – and how to calculate them.
Theoretical Probabilities (reference Chapter 5, section 5.2 from the current text)
a.
b.
c.
d.
Know the basic probability rules.
Know how to find theoretical probabilities with equally likely outcomes.
Know how to find probabilities of events combined with “AND” and “OR.”
Define the term, “mutually exclusive.”
Associations in Categorical Variables (reference Chapter 5, section 5.3 from the current text)
a. Explain what is meant by a conditional probability.
b. Be able to determine whether two events are independent or associated and understand the implications of
making incorrect assumptions about independent events.
The Law of Large Numbers (reference Chapter 5, section 5.4 from the current text)
a. Understand that the Law of Large Numbers allows us to use empirical probabilities to estimate and test
theoretical probabilities.
b. Know how to design a simulation to estimate empirical probabilities.
Probability Distributions for Discrete Variables (reference Chapter 6, section 6.1 from the current text)
a.
b.
c.
d.
Be able to define probability distribution and differentiate between discrete and continuous distributions.
Represent discrete probabilities as tables, graphs, or equations.
Compute the expected value (mean) of discrete distributions.
Represent continuous variables as graphs.
The Normal Model (reference Chapter 6, section 6.2 from the current text)
a. Be able to state when normal model can be used to represent the distribution.
b. Use technology to determine probabilities of some values in normal distributions as well as to determine
values based on probabilities (inverse Normal function).
c. Understand the transformation of the normal distribution to standard normal distribution using z-scores and
be able to justify why this is done.
d. Be able to use z-scores to determine probabilities using both technology and probability table for
standard Normal cumulative probabilities.
The Binomial Model (reference Chapter 6, section 6.3 from the current text)
a. Know the conditions that must be satisfied to use binomial model.
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Department of Mathematics, Kent State University
b. Use technology to find probabilities in binomial models.
c. Know how to compute the expected value (mean) and standard deviation of binomial models.
About Surveys (reference Chapter 7, section 7.1 from the current text)
d. Give definitions of the following terms: population, parameter, census, sample, statistic, estimate,
statistical inference.
e. Be able to explain what is mean by a biased method, sampling bias, and measurement bias. Be able to give
an example of each.
f. Discuss other problems that might occur with sampling.
g. Understand that random sampling reduces bias.
Measuring the Quality of a Survey (reference Chapter 7, section 7.2 from the current text)
a. Explain the difference between accuracy and precision.
b. Explain the difference between p and 𝑝̂
c. Understand what a sampling distribution is
d. Explain how bias and accuracy are measured
The Central Limit Theorem for Sample Proportions
(reference Chapter 7, section 7.3 from the current text)
a. State the Central Limit Theorem for sample proportions and explain its usefulness.
b. Name the 3 conditions necessary before applying the Central Limit Theorem (see p. 305) and be able to check
for them.
c. Use the Central Limit Theorem for Sample Proportions to find the probability that a sample proportion will be
near (or far from) the population value
Hypothesis Testing
(reference Chapter 8, section 8.1 from the current text)
a. Give definitions of the following terms: hypothesis testing, null hypothesis, alternative hypothesis, test
statistic, significance level.
b. Explain what a p-value is.
c. Explain the “main ingredients” in a hypothesis test
p-Value (reference Chapter 8, section 8.2 from the current text)
a.
b.
c.
d.
Learn the difference between a two-tailed and one-tailed hypothesis test
Know the conditions required for calculating an approximate p-Value
Learn how to calculate the p-Value
Interpret the p-value for either a one-tailed or two-tailed hypothesis
Four Steps of Hypothesis Testing (reference Chapter 8, section 8.3 from the current text)
a.
b.
c.
d.
e.
f.
Define what a one proportion z-test is and how it is used
State the null and alternative hypotheses given a situation involving a single population proportion
Check to see if the four conditions for the Central Limit Theorem are satisfied
Compute the standard error and the z-statistic then use technology to find the p-value
Correctly decide whether or not to reject the null hypothesis
Correctly interpret the result of a hypothesis test
Hypothesis Testing: Error Types and Power (reference Chapter 8, section 8.5 from the current text)
a. Understand the types of errors possible in hypothesis testing
b. Know what power in a test is
c. Understand the difference between statistical significance and practical significance
Hypothesis Testing for Population Means (reference Chapter 9, section 9.1, 9.2, and 9.3 from the current text)
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Department of Mathematics, Kent State University
a. be able to examine and understand the characteristics of the behavior of the sample mean; its accuracy, its
precision, and its probability distribution.
- accuracy is measured by the bias
- precision is measured by the standard error
- probability distribution is measured by the shape of the distribution for a continuous variable
b. Be able to check conditions of CLT for sample means
c. Be able to interpret the results of CLT for sample means
- accuracy is measured by the bias
- precision is measured by the standard error
- probability distribution is measured by the shape of the distribution for a continuous variable
(Ohio Transfer Module) Apply principles of effective written and oral communication
Activities and quizzes require students to answer some open-ended questions and to communicate their
mathematical thinking. They work on activities in groups and through that practice communication.
A Broaden their imagination and develop their creativity
Students are challenged to problem solve on daily basis.
Cultivate their natural curiosity and begin a lifelong pursuit of knowledge
Students are challenged to problem solve on daily basis.
Develop competencies and values vital to responsible uses of information and technology op
competencies and values vital to responsible uses of information and technology
Homework assignments are done in MyLabsPlus. The students must master the interface and also statistical
software StatCrunch.
(Ohio Transfer Module) Engage in independent thinking, develop their own voice and vision, and become
informed, responsible citizens
Many examples presented in the course are about important topics such as medical research, environment, and
social sciences. Through these examples students learn about these topics as well.
(Ohio Transfer Module) Improve their understanding of issues and behaviors concerning inclusion,
community and tolerance
Group work in activities promotes team work and collaboration.
Increase their awareness of ethical implications of their own and others’ actions
Students are responsible for contributing in their group and also working by themselves with no help when they work
on individual assignments.
Integrate their major studies into the broader context of a liberal education
Many examples and problems are from the real life studies in social sciences.
Strengthen quantitative reasoning skills
The students will learn many new statistical concepts but the main goal is to understand how these
concepts are used in statistical applications and how the result of statistical analysis are interpreted.
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Department of Mathematics, Kent State University
(Ohio Transfer Module) Understand basic concepts of the academic discipline
Understand the concepts of variables, sampling methods, graphical representation of the data, measures of
center and spread, correlation vs. causation, linear trends, distributions, random experiments, probability
function, normal and binomial models, measuring the survey accuracy and bias, CLT and hypotheses testing for
sample proportions and sample means.
Examples of Detailed Learning Outcomes with Assessment Rubrics
Tests are delivered in MyLabsPlus as multiple choice questions so the rubric is not applicable to tests.
Learning Outcomes
About the data
a.
b.
c.
d.
(reference Chapter 1, section 1.1 and 1.2 from the current text)
Explain the meaning of the word “statistics.”
Distinguish between a variable in algebra and a variable in statistics.
Distinguish between numerical and categorical variables.
Understand methods for coding categorical variables
Categorical Data (reference Chapter 1, sections 1.3 and 1.4 from the current text)
a.
Know how to find and use rates (including percentages) and understand when and why they are more useful than counts for describing and
comparing groups.
b. Understand when it is possible to infer a cause-and-effect relationship.
c.
Explain how confounding variables prevent us from inferring causation, and suggest confounding variables that are likely to occur in some situations.
d. Be able to distinguish between observational studies and controlled experiments.
e. Explain the difference between simple random, stratified, systematic, cluster, and convenience sampling.
1.
Possible Assessment Items for Quizzes and Activities
Kitchenaid wants to administer a satisfaction survey to its current customers. Using their customer database of 3500
customers, the company randomly selects 150 customers and asks them their level of satisfaction with the company.
What type of sampling is used? Justify your answer. What is the sample size? What type of variable will be collected?
If there are 5 levels of satisfaction, how the variable can be coded?
2.
To determine her blood glucose levels, Ann divides up her day into three parts: morning, afternoon, and evening. She
then measures her blood glucose levels at three randomly selected times during each part of the day. What type of
sampling is used? What type of variable will be collected?
3.
You want to poll voters regarding a proposal for a national high speed rail system. Design a sampling method to obtain
the individuals preferences in the sample. Which sampling method would most likely be used in a poll of voters
regarding a proposal for a national high speed rail system: stratified random sampling, convenience sampling, cluster
sampling, systematic random sampling, simple random sampling. Support your choices.
4.
A local public school encourages, but does not require, students to wear uniforms. The principal of the school
compares the grade point averages of students at this school who wear uniforms with the GPAs of those who do not
wear uniforms to determine whether those wearing uniforms tend to have higher GPAs. Is this an observational study
or a controlled experiment? If the principal finds that students who wear uniforms tend to have higher GPAs can he
conclude that the wearing of school uniforms leads to higher GPAs. Why or why not?
Rubric: A – answers completely and accurately to all questions with accurate math writing. For example: n=150
B – one answer is incorrect or minor error in math writing
C – show some level of understanding but some answers completely incorrect
F - does not know sampling methods or variable types, poor math writing
Learning Outcomes
The Normal Model (reference Chapter 6, section 6.2 from the current text)
a.
Be able to state when normal model can be used to represent the distribution.
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Department of Mathematics, Kent State University
b.
c.
d.
1.
Use technology to determine probabilities of some values in normal distributions as well as to determine values based on probabilities (inverse
Normal function).
Understand the transformation of the normal distribution to standard normal distribution using z-scores and be able to justify why this is done.
Be able to use z-scores to determine probabilities using both technology and probability table for standard Normal cumulative probabilities.
Possible Assessment Items for Quizzes and Activities
In 2009, ACT reading scores had a mean of 21.4. Suppose the population standard deviation is 5 and the distribution of
ACT reading scores is approximately normal.
a. Write normal distribution in the format 𝑁(𝜇, 𝜎)
b. What is the probability that a randomly selected person will score between 18 and 22?
c. What is the probability that a randomly selected person will score 25.8 or higher
d. In 2009, what is the approximate reading score for a student who scored in the 80th percentile?
2. Which is more unusual? Assume both distributions are approximately normally distributed: A value of 1.61 from a
distribution with mean 2.17 and standard deviation 0.25 or a value of 68 from a distribution with mean 51 and standard
deviation 7.1. State why the value is more unusual.
Rubric: A – answers accurately to all questions with accurate math writing. For example: N(21.4, 5)
B – incomplete math writing, for example 𝑃(𝑋 < 1.61) = is missing when reporting probabilities.
C – show some level of understanding but some answers completely incorrect , wrong formulas used
F - does not know formulas, how to use them, or how to use technology to compute required values.
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