Download MA111 - Mohawk Valley Community College

MOHAWK VALLEY COMMUNITY COLLEGE
UTICA AND ROME, NEW YORK
COURSE OUTLINE
and
TEACHING GUIDE
INTERMEDIATE STATISTICS
MA 111
Prepared by John Swistak, April, 2016
COURSE OUTLINE
Title:
Intermediate Statistics
Catalog #:
MA 111
Credit Hours:
3
Lecture Hours:
3
Lab Hours:
0
Prerequisites:
Satisfactory completion of MA 110 Elementary
Statistics or an equivalent course.
Catalog Description:
This course is a continuation of elementary statistics (MA 110)
emphasizing confidence intervals and hypothesis testing. Topics
include
single
and
two-sample
analysis,
single
and
multiple
regression, chi-square testing, testing and estimating standard
deviation and variance, one-way and two-way ANOVA, and other topics in
statistics. Emphasis is placed on selecting the proper technique,
satisfying its requirements and correctly reporting the results.
GOALS AND OUTCOMES
COURSE TEACHING GOALS FOR ALL TOPICS:
GOAL A: Use mathematical processes to acquire and convey knowledge.
GOAL B: Systematically solve problems and interpret information or
data.
STUDENT LEARNING GOALS FOR MA111: STATISTICS II
Students successfully completing the course will be able to:
1.
2.
3.
Demonstrate an awareness of the historical development of
statistical methods and techniques and how they relate to various
disciplines
Analyze data using a variety of statistical techniques
Demonstrate an ability to formulate statistical statements, reason
and draw appropriate conclusions from data, and critique
conclusions drawn by others
4. Demonstrate an ability to read common statistical tables.
5. Demonstrate an understanding of the fundamentals of inferential
statistics, including the computation and interpretation of test
statistics, exploration of relationships, and the formulation of
statistically based predictions.
6. Demonstrate an understanding of the fundamentals of probability
based statistical inference, including confidence intervals and
the testing of hypotheses.
7.
8.
9.
Demonstrate the ability to use technological tools (such as a
calculator and/or computer) as they relate to statistical
concepts.
Demonstrate
an
understanding
of
the
course
concepts
by
communicating through appropriate verbal, written, graphical and
other means.
Students will be able to work effectively within a group by
demonstrating openness toward diverse points of view, drawing upon
knowledge and experience of others to function as a group member,
demonstrating skill in negotiating differences and working toward
solutions.
SUNY Learning Outcomes
1. The student will develop well reasoned arguments.
2. The student will identify, analyze, and evaluate arguments as
they occur in their own and other’s work.
3. The student will demonstrate the ability to interpret and draw
inferences from mathematical models such as formulas, graphs,
tables, and schematics.
4. The student will demonstrate the ability to represent
mathematical information symbolically, visually, numerically,
and verbally.
5. The student will demonstrate the ability to employ quantitative
methods such as arithmetic, algebra, geometry, or statistics to
solve problems.
6. The student will demonstrate the ability to estimate and check
mathematical results for reasonableness.
7. The student will demonstrate the ability to recognize the limits
of mathematical and statistical methods.
TOPIC 1.
Estimation
Point estimates for population mean, proportion, Standard deviation,
and variance are discussed.
Confidence intervals for the mean,
proportion, standard deviation, and variance of a population are
constructed.
The relationship between sample size and the error in
the estimate is discussed. Point estimates and confidence intervals
for the difference of the means, proportions, standard deviations, and
variances of two populations are also discussed.
Topic Goal: To help students develop an understanding of the
fundamentals and usefulness of estimating with
confidence.
Student Outcomes:
1.1
1.2
1.3
1.4
The student will:
Define point estimates for the population mean, proportion,
standard deviation, and variance; and the difference of
means, proportions, standard deviations, and variances for
two populations.
Construct the corresponding confidence intervals
Determine sample size for a desired margin of error.
Demonstrate the ability to properly use the t-, chi-square,
and F-distributions as appropriate.
TOPIC 2.
Hypothesis Tests
The basic concepts of hypothesis testing are reviewed. Both single
and two sample hypothesis tests are discussed for means, proportions,
Standard deviations, and variances,.
Topic Goal: To help students develop an understanding of the
fundamentals and usefulness of hypothesis tests of the
population mean, proportion, and variance; and the
difference of means, proportions, standard deviation,
and variances of two populations.
Student Outcomes:
2.1
2.2
2.3
2.4
2.5
The student will:
Conduct a complete hypothesis tests using both the critical
value and p-value approach.
Be able to interpret the p-value of a test.
Distinguish the potential difference between statistical
significance and practical significance.
Distinguish between dependent and independent samples.
Distinguish between Type I and Type II errors, and understand
the power of a test.
TOPIC 3.
Correlation and Regression
The basic concept of linear correlation is introduced.
Linear
regression
is
discussed,
as
well
as
the
coefficient
of
determination. Confidence intervals for β and ρ are constructed’ and
hypothesis tests are performed.
Topic Goal: To help students develop an understanding of the
fundamentals and usefulness of exploring relationships
among quantitative variables for the purposes of model
building and prediction.
Student Outcomes:
The student will:
3.1
Examine quantitative data occurring in many areas such as
science, business, economics, social sciences, and health
sciences.
3.2
Recognize
the
response
(dependent)
and
explanatory
(independent) variable as suggested by the data.
Recognize outliers and their effects.
Recognize that correlation is not cause and effect.
Calculate and interpret the coefficient of determination.
Construct confidence and prediction intervals for the
estimate and interpret their meanings.
Calculate residuals and use them to verify the assumptions of
the regression.
3.3
3.4
3.5
3.6
3.7
TOPIC 4.
Relationships between variables in which at least one is
not quantitative
The concept of the chi-square tests is introduced.
Expected
frequencies and degrees of freedom are computed. Hypothesis tests are
performed.
Topic Goals: To help students develop an understanding of the
fundamentals and usefulness of exploring relationships
between
variables
in
which
at
least
one
is
categorical.
Student Outcomes:
The student will:
4.1
Construct a two-way table in order to calculate expected and
observed frequencies.
4.2
Construct and interpret complete hypothesis tests for
homogeneity and for the independence of two variables.
Construct and interpret a complete hypothesis test to
determine if a set of observations fits a specified
distribution.
4.3
TOPIC 5.
Analysis of Variance (ANOVA)
Comparing several means at once as opposed to comparing in pairs is
discussed.
A calculation of the sums of squares is introduced to
create the ANOVA table.
Experimental design, blocking and special
cases are covered. Two-way ANOVA is also covered.
Topic Goal: To help students develop an understanding of the
fundamentals and usefulness of Analysis of Variance.
Student Outcomes:
5.1
5.2
5.3
5.4
5.5
5.6
5.7
The student will:
Construct and interpret the ANOVA table.
Construct and interpret a complete hypothesis test comparing
several means.
Understand the difference between variation within and among
samples.
Be able to check assumptions of the test.
Understand the rudiments of experimental design as an
application of ANOVA.
Describe main effects and interactions, and test hypotheses
about them.
Construct and interpret interaction plots.
TEACHING GUIDE
Title:
Intermediate Statistics
Catalog #:
MA 111
Credit Hours:
3
Lecture Hours:
3
Lab Hours:
0
Prerequisites:
Satisfactory completion of MA 110 Elementary
Statistics or an equivalent course.
Catalog Description:
This is a second course in statistics emphasizing confidence intervals
and hypothesis testing. Topics include single and two-sample analysis,
single and multiple
regression, chi-square testing, testing and
estimating standard deviation and variance, and one-way and two-way
ANOVA. Emphasis is placed on selecting the proper technique,
satisfying its requirements and correctly reporting the results.
Text:
Elementary Statistics, Second Edition, Navidi and
Monk, McGraw-Hill, 2016.
Part 2 of the MVCC
custom printing.
Calculator Usage:
A statistical calculator equivalent to the TI-83
is required.
Course Schedule:
The Required Topics identified in the Course
Outline account for 41 hours of instruction. The
teaching guide allows four hours for in-class
assessment
of
student learning. A two-hour
comprehensive final exam covering the required
topics will be given.
Required Topics:
(41 hours)
Chapter 8: Confidence Intervals
8.1 Confidence intervals for
deviation known.
8.2 Confidence intervals for
deviation Unknown.
8.3 Confidence intervals for
8.4 Confidence intervals for
8.5 Determining which method
(5 hours)
a population mean, standard
a population mean, standard
a population proportion.
a standard deviation.
to use.
Chapter 9: Hypothesis Testing
(7 hours)
9.1
9.2
Basic principles of Hypothesis testing(treat as review).
Hypothesis tests for a Population Mean, Standard Deviation
known.
9.3 Hypothesis tests for a Population Mean, Standard Deviation
unknown.
9.4 Hypothesis tests for Proportions.
9.5 Hypothesis tests for a Standard Deviation.
9.6 Determining which method to use.
9.7 Power.
Chapter 10: Two-Sample Confidence Intervals
(6 hours)
10.1 Confidence Intervals for the Difference Between Two Means:
Independent Samples
10.2 Confidence Intervals for the Difference Between Two
Proportions
10.3 Confidence Intervals for the Difference Between Two Means:
Paired Samples
Chapter 11: Two Sample Hypothesis Tests
(8 hours)
11.1 Hypothesis Tests for the Difference Between Two Means:
Independent Samples.
11.2 Hypothesis Tests for the Difference Between Two Proportions.
11.3 Hypothesis Tests for the Difference Between Two Means:
Paired Samples.
11.4 Hypothesis Tests for Two Population Standard Deviations.
11.5 The Multiple Testing Problem.
Chapter 12: Tests with Qualitative Data
(4 hours)
12.1 Testing Goodness of Fit
12.2 Tests for Independence and Homogeneity
Chapter 13: Inference in Linear Models
13.1 Inference on the Slope of the Regression Line.
13.2 Inference About the Response.
(5 hours)
Chapter 14: Analysis of Variance
(6 hours)
14.1 One-Way Analysis of Variance.
14.2 Two-Way Analysis of Variance.
Note: Certain of the material in Chapters 8 and 9 should have been
covered in MA 110. See the MA 110 Outline).