Download 1342 Course Outline

Department of Mathematics
Math 1342: Elementary Statistical Methods
COURSE OUTLINE
(Revised August 2016)
3 hour lecture course / 48 hours per semester
Textbook: Elementary Statistics, A step by step Approach, 9th Edition, Bluman.
ISBN: 978-0-781-3633-7
Catalog Description: MATH 1342 Elementary Statistical Methods. Topics include
Collection, analysis, presentation and interpretation of data, and probability. Analysis includes
descriptive statistics, correlation and regression, confidence intervals and hypothesis testing. Use
of appropriate technology is recommended.
Prerequisites: A grade of C or better in Math 0312 or a grade of C or better in MATH 1314 or
its equivalent or an acceptable placement test score.
Course Intent: This course is intended for students primarily in health sciences and business
rather than math or science majors. It consists of concepts, ideas, and applications of statistics
rather than a theory course.
Audience: This course is for students who require a statistics course as a prerequisite for further
study.
Course Student Learning Outcomes (SLO):
1. Explain the use of data collection and statistics as tools to reach reasonable conclusions.
2. Recognize, examine and interpret the basic principles of describing and presenting data.
3. Compute and interpret empirical and theoretical probabilities using the rules of probabilities and
combinatorics.
4. Explain the role of probability in statistics.
5. Examine, analyze and compare various sampling distributions for both discrete and continuous random
variables.
6. Describe and compute confidence intervals.
7. Solve linear regression and correlation problems.
8. Perform hypothesis testing using statistical methods.
Course Objectives: Upon completion of this course, a student should be able to:
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Demonstrate knowledge of statistical terms.
Understand the different between descriptive and inferential statistics.
Identify: types of data, measurement level of variables, and four basic sampling techniques.
Construct the relative frequency table from a given set of ungroup data.
Know and use the different graphs: histogram, frequency polygon, Ogives, Pareto, and pie to present data.
Compute the mean, median, mode, midrange, range, variance, and standard deviation.
Identify the various measures of position such as percentiles, deciles, and quartiles.
Find the total number of outcomes in a sequence of events using tree diagram and multiplication rule.
Understand the use of permutation and combination rules.
Determine sample spaces and find the probability of an event using classical probability.
Find the probability of compound events using addition and/or multiplication rules.
Find the conditional probability of an event
Construct a probability distribution for a random variable
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Find the mean, variance, and expected value for a probability distribution function.
Find the exact probability for X successes in n trial of a binomial experiment.
Find the mean, variance, and standard deviation for binomial distribution.
Identify the properties of the normal distribution.
Find the area under the normal curve, given various z values.
Find probabilities for a normally distributed variable by transforming it into a standard normal variable.
Find specific data values for given percentages using the standard normal distribution.
Apply the central limit theorem to solve problems involving sample means.
Use the normal approximation to compute probabilities for a binomial variable.
Find a confidence interval for the mean when  is known or n  30.
Determine the minimum sample size for finding a confidence interval for the mean.
Find a confidence interval for the mean when  is unknown and n < 30.
Find a confidence interval for proportion.
Determine the minimum sample size for finding a confidence interval for a proportion.
Find a confidence interval of variance and standard deviation.
Understand the definitions used in hypothesis testing.
State null hypothesis and alternative hypothesis.
Understand the terms: type I error and type II error, test criteria, level of significance, test statistic.
Find the critical values for the z-test, t-test, and  -test.
Test hypothesis for: means (large and small sample), proportions, variance, and standard deviation.
Draw scatter plot for a set of ordered pairs.
Compute the correlation coefficient and the coefficient of determination.
Compute the equation of the regression line by using the least square method.
Test a distribution for goodness of fit using chi-square.
Test independence and homogeneity using chi-square.
Use the one-way ANOVA technique to determine if there is a significant difference among three or more
means.
40. Determine differ in means using the Scheffe’ or Tukey test if the null hypothesis is rejected in the ANOVA.
Course Outline: Instructors may find it preferable to cover the course topics in the order listed below.
However, the instructor may choose to organize topics in any order, but all material must be covered.
APPROXIMATE TIME
Unit I – The Nature of Probability and Statistics
(3 hours)
TEXT REFERENCE
Sections: 1.1-1.5
This unit covers an introduction to statistics, descriptive and inferential statistics, variables and types of
data, data collection, sampling techniques, and uses and misuses of statistics. A technology discussion is
included.
Unit 2 – Frequency Distribution and Graphs
Sections: 2.1-2.3
(3 hours)
This unit covers data in frequency distributions and tables, graphs of frequency polygons,
histograms, ogives, pareto charts, and time series. quartiles, and outliers.
Unit 3 – Data Description
(6 hours)
Sections: 3.1-3.4
This unit covers measures of central tendency, measures of variation, and measures of position. Topics
include measures of central tendency, measures of variation, and measures of position. Included in these
topics are the math concepts of mean, median, mode, distribution shapes, range, variance, standard
deviation, coefficient of variation, Chebyshev’s theorem, z score, percentiles, deciles,
Unit 4 –Probability and Counting Rules
(4.5 hours)
Sections: 4.1-4.5
This unit begins with the introduction to probability as a chance concept. The basic concepts of
probability covered are probability experiments, sample spaces, the addition and multiplications rules,
and conditional probabilities. Also, counting rules, permutations and combinations are discussed.
Unit 5 – Discrete Probability Distributions
(4.5 hours)
Sections: 5.1-5.4.
This unit gives an introduction to distribution theory and explains the concepts and applications of a
probability distribution. Topics include mean and variance of discrete random variables and the binomial
distribution.
Unit 6 – Normal Distribution
(6 hours)
Sections: 6.1-6.4
This unit begins with properties of a normal distribution. Topics include the standard normal distribution,
application of the normal distribution, the central limit theorem, and normal approximation to the
binomial distribution.
Unit 7 – Confidence Intervals and Sample size
(6 hours)
Sections: 7.1-7.4
This unit starts with an introduction to inferential statistics as related to estimation. Topics include
confidence intervals for the mean (standard deviation of population known and
(n  30), sample size, confidence intervals for mean (sigma unknown and ( n < 30), confidence intervals
and sample size for proportions, and confidence intervals for variances and standard deviation.
Unit 8 – Hypothesis Testing
(6 hours)
Sections: 8.1-8.4
This unit begins with an introduction to the concepts involved with statistical hypothesis testing. Topics
include steps in hypothesis testing of the z-test for mean and proportion, and the t-test for means using the
traditional and p-value methods. A chi-squared test for variance and standard deviation is also included.
Unit 9 – Testing the difference
Sections: 9.1-9.5
(4.5 hours)
This unit begins with testing the difference between two means, two proportions, and two
variance
Unit 10 – Correlation and Regression
Sections: 10.1-10.3
(4.5 hours)
This unit begins Scatter Plots and correlation. Topics include regression, line best fit, and
coefficient of determination of standard error of the estimate
Resource Materials: Any student enrolled in Math 1342 at HCCS has access to the Academic
Support Center where they may get additional help in understanding the theory or in improving
their skills. The Center is staffed with mathematics faculty and student assistants, and offers
tutorial help, video tapes and computer-assisted drills. Also available is a student’s Solutions
manual which may be obtained from the bookstore.
NOTICE: Students who repeat a course three or more times may soon face significant
tuition/fee increases at HCC and other Texas public colleges and universities. If you are
considering course withdrawal because you are not earning passing grades, confer with your
professor / counselor as early as possible about your study habits, homework, test-taking skills,
attendance, course participation, and tutoring or other assistance that is available.
Americans with Disabilities Act (ADA): Any student with a documented disability (e.g.,
physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Disability Services Office at the respective college at the
beginning of each semester. Faculty are authorized to provide only the accommodations
requested by the Disability Support Services Office.