Download Introduction to Statistics - Arkansas Northeastern College

MA14033 – Introduction To Statistics
Math/Science Department
Arkansas Northeastern College
Departmental Syllabus
I.
Course Catalog Description
“An introduction to the use and language of statistics which is open to all disciplines. Topics include
measures of central tendency, measures of variability, grouping of data and drawing graphs, probability,
normal distributions, hypothesis testing, estimation, T-tests, F-tests, regression, correlation, prediction and
Chi-square tests.”
II.
Course Rationale
In this course, you will learn to recognize different types of data and what statistical procedures are
appropriate to use on different types of data. You will also learn how to graph data in a meaningful
fashion. To help you understand the fundamentals of statistics, you will also learn about basic probability.
Throughout the course, you will be encouraged to develop a “statistical eye,” so that you can quickly
make educated guesses about data sets without the need to go through complex statistical calculations.
Finally, you will learn to use modern tools of analysis, such as the hand-held calculator, to perform your
calculations quickly and accurately.
III.
Course Objectives
Students will be provided the opportunity to explain, describe, discuss, recognize, and/or apply knowledge
and understanding of the following:
1. types and characteristics of data and how to summarize and graph data
2. measures of center and measures of variation
3. the major issues and concerns in probability
4. how to analyze data drawn from random variables and binomial distributions
5. the properties and uses of the normal distribution
6. the relationship between estimates and sample size
7. how to analyze data based upon populations, single samples, and multiple samples
8. the uses of correlation and regression
9. the uses of the goodness-of-fit test and contingency tables
IV.
Course Prerequisites
A “C” or above in MA 14043 College Algebra.
V.
Course Credits
Students earn 3 credit hours upon successful completion of this course.
VI.
Required Texts and Materials
Elementary Statistics Using the Ti-83/84 Plus Calculator. 3rd ed., by Mario F. Triola (Addison-Wesley, 2011)
VII. Supplementary Materials
Texas Instruments TI-83 Plus or TI-84 Plus calculator.
Access to a computer and the internet. (Access is available on the ANC campus.)
VIII.
Course Policies: Grades
Grades of "Incomplete":
The current College policy concerning incomplete grades will be followed in this course. Incomplete
grades are given only in situations where unexpected emergencies prevent a student from completing the
course and the remaining work can be completed the next semester. Your instructor is the final authority on
whether you qualify for an incomplete. Incomplete work must be finished by the end of the subsequent
semester or the “I” will automatically be recorded as an “F” on your transcript.
IX.
Course Policies: Technology and Media
Email: Arkansas Northeastern College has partnered with Google to host email addresses for ANC
students. myANC mail accounts are created for each student enrolled in the current semester and is the
email address your instructor will use to communicate with you. Access your email account by going to
http://mail.google.com/a/smail.anc.edu and using your first and last names, separated by a period for your
username. Your default password is the last six digits of your Student ID. If you cannot access your
student email, contact the MITS department at 762-1020 ext 1150 or ext 1207 or send an email to
[email protected].
Internet This course has a web component on myANC. The first day handout, study guides,
announcements, and reminders will be posted on myANC.
Classroom Devices All cell phones must be turned off during class. No texting in class (sending or
checking for text messages)!
Computer Labs: In addition to general-purpose classrooms, a number of computer laboratories are
provided for instructional and student use. These networked laboratories are state-of-the-art and fully
equipped with computers, printers, Internet connections and the latest software. The labs are open to
students enrolled in one or more credit hours at the College.
Technology Support: A lab assistant is generally present in the computer lab in B202 for assistance in
using the College computers. These assistants cannot help you with course assignments; specific questions
regarding the technology requirements for each course should be directed to the instructor of the course.
Problems with myANC or College email accounts should be addressed by email to
[email protected].
Course Policies: Student Expectations
Disability Access: Arkansas Northeastern College is committed to providing reasonable accommodations
for all persons with disabilities. This First Day Handout is available in alternate formats upon request.
Students with disabilities who need accommodations in this course must contact the instructor at the
beginning of the semester to discuss needed accommodations. No accommodations will be provided until
the student has met with the instructor to request accommodations. Students who need accommodations
must be registered with Johnny Moore in Statehouse Hall, 762-3180.
Professionalism Policy: Please make every effort to be on time!!! Excessive tardiness (more than 3 times
during the semester) will not be tolerated. "Coming and going" is disruptive to the learning process and
also will not be tolerated. Per classroom etiquette; mobile phones, iPods, etc. must be silenced during all
classroom lectures. Those not heeding this rule will be asked to leave the classroom/lab immediately so as
to not disrupt the learning environment. Please arrive on time for all class meetings. Do not bring food to
eat during class time.
Academic Integrity Policy:
Academic dishonesty in any form will not be tolerated. If you are uncertain as to what constitutes academic
dishonesty, please consult the Academic Integrity Policy in ANC’s Student Handbook
(http://www.anc.edu/docs/anc_handbook.pdf) for further details. Students are expected to do their own
work. Plagiarism, using the words of others without express permission or proper citation, will not be
tolerated. Any cheating (giving or receiving) or other dishonest activity will, at a minimum, result in a zero
on that test or assignment and may be referred, at the discretion of the instructor, to the Department Chair
and/or Vice President of Instruction for further action.
Learning Assistance Center: The Learning Assistance Center (LAC) is a free resource for ANC students.
The LAC provides drop-in assistance, computer tutorials and audio/visual aids to students who need help in
academic areas. Learning labs offer individualized instruction in the areas of mathematics, reading, writing,
vocabulary development and college study methods. Tutorial services are available on an individual basis
for those having difficulty with instructional materials. The LAC also maintains a shelf of free materials
addressing specific problems, such as procedures for writing essays and term papers, punctuation reviews,
and other useful materials. For more information, visit the LAC website at http://www.anc.edu/LAC or
stop by room L104 in the Adams/Vines Library Complex.
Other Student Support Services: Many departments are ready to assist you reach your educational goals.
Be sure to check with your advisor; the Learning Assistance Center, Room L104; Student Support Services,
Room S145; and Student Success, Room L101 to find the right type of support for you.
X.
Unit and Instructional Objectives
Unit I: Descriptive Statistics & Probability (Course Objectives Ch.1, Ch.2, Ch3, and Ch.4)
Rationale: In this unit, key terms and basic concepts of descriptive statistics and probability will be
studied. This will provide the foundation for statistical thinking.
At the conclusion of this unit, the student will have had to opportunity to do the following:
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Define statistics, data, population, census, and sample.
Given a value and its description, determine whether the given value is a statistic or a parameter, from
a discrete or continuous data set, or if it is quantitative or categorical data.
Given the description of a data set, determine which of the four levels of measurement (nominal,
ordinal, interval, ration) is most appropriate.
Given the description of a study, determine if it is an observational study or an experiment.
Given the description of a study, determine which type of sampling was used to collect the data:
random, systematic, convenience, stratified, or cluster.
Given the description of a sampling, determine if it is a random sample or a simple random sample.
Given the description of a sampling, determine if the sample data were collected in an appropriate
manner. If not, indicate that the data is useless.
Given a data set, construct a frequency distribution, relative frequency distribution, and/or a
cumulative frequency distribution.
Given a frequency distribution in which classes were used, identify the class width, class midpoints,
and class boundaries.
10. Given a data set, construct a frequency distribution, and then draw a histogram for that distribution
both by hand and by using a graphing calculator.
11. Given a histogram, determine the sample size, center, outliers, class width and class limits, variation of
data, gaps in the data, skewness, frequency polygon, and answer specific questions about the data.
12. Use frequency histograms and polygons to compare two sets of data.
13. Recognize and critique misleading graphs.
14. Given a set of data, construct a stemplot, a dotplot, an ogive, a Pareto chart, pie chart and/or a
scatterplot by hand and by using a graphing calculator (if possible).
15. Given any of the above charts, analyze any trends in the data and decide which chart best depicts the
data.
16. Given a set of data, calculate the mean median, mode, and midrange (by hand and with a graphing
calculator) and decide if these measures of central tendency are meaningful statistics.
17. Given a frequency distribution, calculate the mean.
18. Given a set of data, calculate the measure of variation: range and sample standard deviation (by hand
and by using a graphing calculator). Indicate the proper units on these measures.
19. Given a set of data, calculate the variance. Include proper units.
20. Use the standard deviation to describe the variation of the data values and the effects of any outliers on
the standard deviation.
21. Use the standard deviation to compare the variation in two different data sets having the same scale
and units and approximately the same mean.
22. Use the Empirical Rule for data sets that are nearly Normal to discuss the variation of the data.
23. Use Chebyshev’s Theorem to discuss the variation of a set of data.
24. Given the mean and standard deviation, calculate the z-score of any data value (a measure of relative
standing) and determine if a data value is ordinary or unusual.
25. Given a data set, find a specific percentile or quartile.
26. Given a set of data, construct a 5-Number Summary and a Boxplot and use them to compare two sets
of data.
27. Given a set of data, determine any outliers and then construct a modified boxplot.
28. Define event, simple event, sample space, and the probability of an event.
29. Given a description of an even and its sample space, calculate the probability of that event.
30. Define equally likely outcomes, the Law of Large Numbers, independent events and complementary
events.
31. After calculating the probability of an event, determine if the event is unusual.
32. Given the description of an event, calculate the actual odds against the event, actual odds in favor of
the event, and the payoff odds against the event.
33. Given the description of a compound event, use the Addition Rule, if it applies, to calculate the
probability of event A or event B occurring.
34. Given two events, determine whether the two events are mutually exclusive (disjoint) for a single trial.
35. Given an event, find the complement event.
36. Given a pair of events, determine if they are independent events.
37. Use the Multiplication Rule (if it applies) to find the probability that event A occurs in the first tiral
and event B occurs in the second trial.
38. Calculate the probability of at least one of some event.
39. Calculate the value of a condiont probability.
40. Use simulations to find probabilities.
41. Use the Fundamental Counting Rule to calculate the number of ways a sequence of events can occur.
42. Calculate the number of permutations and combinations of n items taken r at a time.
43. Given the description of an experiment, determine if factorials, combinations, or permutations should
be used to calculate the total number of outcomes.
44. After calculating the total number of outcomes of an experiment by using counting techniques,
calculate the probability of one outcome.
Unit II: Distributions & Inferential Statistics (Course Objectives Ch.5, Ch.6, Ch.7, Ch.8, Ch.9, Ch.10, and
Ch.11)
Rationale: A goal of statistics is to make inferences, or generalizations, about a population based on a
sample. Unit 2 uses inferential statistics to estimate a population parameter and to test a hypothesis or
claim about a population parameter.
At the conclusion of this unit, the student will have had the opportunity to do the following:
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30.
Given a description of a random variable, classify it as discrete or continuous.
Given a description and a table of data values and their corresponding probabilities, determine whether
it is a probability distribution. If not, identify the requirements that are not satisfied.
Given a probability distribution, find the mean, variance, and standard deviation for the probability
distribution.
Identify unusual results with probabilities using the Range Rule of Thumb or the Rare Event Rule for
Inferential Statistics.
Given a probability distribution, find the expected value.
Given a description of a procedure, determine if it results in a binomial distribution.
Given a binomial distribution, calculate the probability of an event using the Binomial Probability
Formula, a graphing calculator, and by using a table.
Given a binomial distribution, calculate the mean and standard deviation. Use the range rule of thumb
to find the maximum and minimum usual values.
Given the description of a Poisson distribution, find the probability of an event.
Define a uniform distribution of a continuous random variable.
Given the density curve for a uniform distribution, find the probability of an event.
Given a standard normal distribution and a graphing calculator, find the probability (or area under its
density curve) corresponding to different z-scores.
Given a known area under the density curve of a standard normal distribution, find the z-score and
critical value using a graphing calculator.
Given a nonstandard normal distribution, convert values to standard z-scores and use the formulas for
the standard normal distribution for calculations.
Given a data set, find the sampling distribution of the mean, sampling distribution of the variance, and
sampling distribution of the proportion.
Apply the Central Limit Theorem.
Use a sampling proportion to estimate a population proportion. Interpret the confidence interval for
the population proportion.
Given sample data and confidence level, construct the confidence interval estimate of the population
proportion.
Given specific data, find the minimum sample size required to estimate a population proportion or
percentage.
Given a confidence level and sample data, find the margin of error and confidence interval for
estimating the population mean.
Determine the sample size required to estimate the population mean, given a desired margin of error.
Given a confidence level and sample data determine if the normal distribution or Student t distribution
should be used to calculate the margin of error.
Given a confidence level and sample data, find a confidence interval for the population standard
deviation.
Determine the sample size necessary to estimate the standard deviation for a given confidence level.
Define hypothesis and hypothesis test.
Given a stated claim, identify the null hypothesis and alternative hypothesis and express them in
symbolic form.
Given a stated claim and sample data, calculate the value of the test statistic.
Define one-tailed test, two-tailed test, and P-value.
Define errors in hypothesis tests: Type I errors and Type II errors.
Demonstrate the ability to test a claim about a proportion, mean, and standard deviation.
31. Demonstrate the ability to make inferences about two proportions and two means for independent
samples.
32. Demonstrate the ability to make inferences about two proportions and two means for dependent
samples.
33. Use the F-test to compare two population variances.
34. Define and calculate a linear correlation coefficient and determine the strength of the linear correlation
between paired quantitative x and y values in a sample.
35. Given a collection of paired sample data, calculate the equation of a regression line and then use this
line to predict the value of one of the variables.
36. Use the Goodness-of-Fit Test to test the hypothesis that an observed frequency distribution fits some
clamed distribution.
37. Given a contingency table, perform a Test of independence.
38. Given a contingency table in which samples have been drawn from different populations, perform a
Test of Homogeneity.
XI.
Assessment
The final exam will be comprehensive.