MAT 204 - INTRODUCTION TO STATISTICS - Chesapeake College

MAT 204
INTRODUCTION TO STATISTICS
FALL 2009
Brenda J. Bloomgarden
Associate Professor - Mathematics
Chesapeake College
Wye Mills, MD 21679

MAT 204 INTRODUCTION TO STATISTICS Fall 2009
Chesapeake College Course Outcomes
Course Number and Title: MAT 204, Introduction to Statistics
Program: General Education
Students will be able to:
Learning Outcomes
1. Classify data and identify appropriate experimental designs
2. Display data using graphs
3. Use measures of central tendency and measures of variation
4. Solve problems using probability rules.
5. Solve application problems involving discrete probability distributions
6. Use technology / tables to solve problems involving the normal distribution
7. Draw conclusions or make predictions from data using inferential statistics.
8. Use a graphing calculator and/or a computer program to solve statistical problems.
Assessment Protocols: Homework
Chapter Tests
Group Projects
Computer Project
Final Exam
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
I. INSTRUCTOR: Mrs. Brenda Bloomgarden – College extension 328 (Voice Mail)
Home: 410-778-0743 E-Mail: bbloomgarden@chesapeake.edu
II. OFFICE HOURS Mondays & Wednesdays 11:30 am - 12:30 am Office LRC -107
Tuesdays & Thursdays 11:30 am - 12:30 am Office LRC -107
Tuesdays 2:30 – 3:30 pm Office LRC -107
III. CLASS MEETING TIMES:
MAT 204 - 101 Mondays & Wednesdays 10:00 am to 11:15 pm in room HEC -210
MAT 204 - 102 Mondays & Wednesdays 1:00 pm to 2:15 pm in room HEC -210
MAT 204 – 103 Tuesdays & Thursdays 10:00 pm to 11:15 pm in room HEC -210
MAT 204 – 104 Tuesdays & Thursdays 1:00 pm to 2:15 pm in room HEC -210
IV. COURSE DESCRIPTION:
An introduction to probability and statistics. Topics included are probability, organization of
data, sampling methods, measures of central tendency and variability, probability
distributions, and hypothesis testing. Three hours per week, 3 credits.
Prerequisite:
Appropriate score on the mathematics placement test, or successful completion of MAT 032.
V. TEXTBOOK:
Elementary Statistics, Picturing the World, Fourth Edition, by Ron Larson and Betsy Farber,
2009. Prentice-Hall, Inc., Upper Saddle River, NJ 07458. This textbook is bundled in a
Special Package that includes the Student Study Pack and the MyMathLab.
ISBN 0321587111
VI. INTRODUCTION:
The primary objective of this course, Introduction to Statistics, is to introduce some basic
statistical concepts to college students. Since statistics has applications in many areas such as
business, science, medicine, and education, examples have been substituted for mathematical
proofs. Graphing calculators and computer software will be used to further illustrate many of
the concepts.
For this three-credit course the average student should plan to spend AT LEAST six hours
per week outside of class working on assignments in addition to the in-class lectures.
Students whose mathematics background is below average, or who normally work at a slower
than average pace, should schedule more time in order to keep up with the course material. If
you need extra help, please see me early in the semester. We would like to see you succeed
and there is extra tutoring available.
NOTE: College policy prohibits young children from accompanying parents to class.
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
VII. GRADES:
This course consists of all or parts of chapters #1 through#10 in the assigned textbook. The
following syllabus outlines in detail the material that will be presented from each of the
chapters. The numerical final course grade will be computed as indicated in the following
distribution, and letter grades will be assigned as follows.
Components of Final Grade Letter Grade
In-Class Activities 5% A : 90% - 100%
Homework 5% B 80% - 89%
Quiz Average 65% C : 70% - 79%
Final Examination 25% D : 60% - 69%
F : less than 60%
VIII ATTENDANCE:
Students whose attendance is sporadic often do not do well because of the nature of the
course content. In addition, since attendance and participation constitute 5% of the
student's final grade, (one-half of a letter grade) it is to the benefit of each student to be
present at every class session. Most students need guidance in understanding the
procedures involved in developing a new mathematical process and regular attendance
tends to improve understanding. If you find yourself unable to keep up with the class,
make an appointment to see the instructor outside of class time. It is the student's
responsibility to make up any work missed due to an absence for any reason.
IX. WRITING ASSIGNMENT:
Consistent with Chesapeake College’s program of “Writing Across the Curriculum”,
students will be expected to write properly formatted and informative essays to
demonstrate understanding of various portions of the course material.
X. TECHNOLOGY
Students will be expected to use a TI-83+ or TI-84+ calculator for some assignments in
this course. Also they will use the Microsoft Excel computer program to analyze and
display data they have collected. Students who successfully complete the assigned
“Computer Project” will have their lowest quiz grade omitted from the calculation of
their “Quiz Average”.
XI. TESTING:
Dates for quizzes will be announced. Students are expected to be present for class on days
for which quizzes are scheduled. Make up quizzes will be given only in the case of a
documented emergency, and then will be scheduled and graded at the instructor's
convenience. Students will have the opportunity to have a missed quiz grade, OR their
lowest quiz grade omitted if they successfully complete the Computer Project.
If a student is absent prior to a scheduled quiz, he/she will still be expected to take
the quiz at the scheduled time and is expected to contact a classmate or the
instructor to obtain the information required in order to prepare for the quiz.
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
MAT 204 - INTRODUCTION TO STATISTICS
COURSE OUTLINE
Chapter TOPIC Pages
One Introduction to Statistics 1 - 37
Two Descriptive Statistics 38 - 137
Three Probability 128 - 191
Four Discrete Probability Distributions 192 - 237
Five Normal Probability Distributions 238 - 305
Six Confidence Intervals 306 - 361
Seven Hypothesis Testing with One Sample 362 - 435
Eight Hypothesis Testing with Two Samples 436 - 491
Nine Correlation and Regression 492 - 549
Ten Chi Square Tests and the F-Distribution 550 - 609
Course Review and Final Examination All Chapters
The quizzes will cover the subject matter of each chapter, and quizzes for specific sections may be
combined so as to maximize course effectiveness. The above outline may be modified slightly as
necessary to accommodate student needs and to permit possible computer and/or video
demonstrations.
A brief description of the Objectives for each chapter and the Homework Assignments are detailed
on the following pages.
Homework Assignments will be due before each quiz or as requested by the instructor and will
include those sections covered in the previous class lecture. It is expected that each student will be
able to solve ALL of the exercise problems in each section covered, even though only part of the
exercise problems are specifically assigned.
Homework is to be legible and for each problem the homework should include given data, any
required calculations and the final answer. Credit will not be given for answers only. The answers
to the odd numbered problems are given in the back of the textbook, and the complete solutions to
most of them are presented in the “Student Solutions Manual”.
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES
After completing each chapter the student should be able to accomplish the following:
Chapter One Introduction to Statistics
OBJECTIVES:
a. Define statistics.
b. Distinguish between a population and a sample and between a parameter and a statistic.
c. Distinguish between descriptive statistics and inferential statistics.
d. Distinguish between qualitative data and quantitative data.
e. Classify data with respect to the four levels of measurement: nominal, ordinal, interval, and
ratio.
f. Identify the characteristics of a confounding variable, blind experiment, double-blind
experiment, randomization, and replication in an experimental design
g. Design a statistical study.
h. Collect data by performing an experiment, using a simulation, taking a census, or using a
sample.
i. Create a sample using random sampling, stratified sampling, cluster sampling, systematic
sampling, and convenience sampling.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 1.1 Problems #1-4, 7-10, 11-14, 18,25-28, 31, 32, 37, 38 Pages 8 - 10
Sec. 1.2 Problems #2-5, 9-12, 13, 16, 18, 21-24 Pages 15 - 16
Sec. 1.3 Problems #1-4, 6-9, 11-14, 15, 18-22, 29, 30, 33, 34 Pages 25 - 27
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Two Descriptive Statistics
OBJECTIVES:
a. Construct a frequency distribution including midpoints, relative frequencies, and
cumulative frequencies.
b. Construct frequency histograms, frequency polygons, relative frequency histograms, and
cumulative frequency graphs (ogives).
c. Graph quantitative data sets using stem-and-leaf plots and dot plots.
d. Graph qualitative data using pie charts and Pareto charts.
e. Graph paired data sets using scatter plots and time series charts.
f. Find the mean, median, and mode of a population and a sample.
g. Find the weighted mean and the mean of the frequency distribution.
h. Describe the shape of a distribution as symmetric, uniform, or skewed.
i. Find the range of a set of data.
j. Find the variance and the standard deviation of a population and of a sample.
k. Use the Empirical Rule and Chebychev's Theorem to interpret standard deviation.
l. Approximate the sample standard deviation for grouped data.
m. Find the first, second, and third quartiles of a data set.
n. Find the interquartile range of a data set.
o. Represent a data set graphically using a box-and-whisker plot.
p. Interpret other fractiles such as percentiles and deciles.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 2.1 Problems #1-10, 14, 16, 17, 19-21, 25-27, 30, 37, 38, 41 Pages 49 - 53
Sec. 2.2 Problems #1, 2, 4-10, 13, 14, 17, 18, 23, 24, 29, 30 Pages 62 - 65
Sec. 2.3 Problems #1-10,13, 14, 17, 18, 23, 26, 35-37, 41, 42, 47, 48
Pages 74 - 78
Sec. 2.4 Problems #1-10, 13, 14, 17, 18, 23, 24, 27-32, 35-37, 43, 45, 46*, 51
* Use data from problem #3, instead of problem #21 Pages 92 - 99
Sec. 2.5 Problems #1-12, 21, 22, 29-35, Pages 109 - 112
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Three Probability
OBJECTIVES:
a. Identify the sample space of a probability experiment and identify simple events.
b. Use the Fundamental Counting Principle to find the number of ways two or more events
can occur.
c. Distinguish among classical probability, empirical probability, and subjective probability.
d. Use Tree Diagrams or The Fundamental Counting Principle for probability applications
e. Identify and use properties of probability.
f. Find the probability of an event given that another event has occurred.
g. Distinguish between independent events and dependent events.
h. Use the multiplication rule to find the probability of two events occurring in sequence.
i. Use the multiplication rule to find conditional probabilities.
j. Determine if two events are mutually exclusive.
k. Use the addition rule to find the probability of two events.
l. Find the number of ways a group of objects can be arranged in order. (permutations)
m. Find the number of ways to choose several objects from a group without regard to order.
(combinations)
n. Use counting principles to find probabilities.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 3.1 Problems #1-8, 11-16, 18, 20, 21-24, 27-30, 31-34,
41 (see #37-#40), 44, 46, 48, 52, 55, 57, 60, 64-67 Pages 142 – 147
Sec. 3.2 Problems #1-8, 9, 11, 13, 15, 16, 17, 21-25, 27, 37, 38 Pages 154 - 159
Sec. 3.3 Problems #1-4, 9-10, 13-15, 20, 21, 23, 24, 29 Pages 165 - 169
Sec. 3.4 Problems #1-6, 9-12(show work), 15-17, 19-21, 23-27,
29, 32, 36, 43 Pages 178 - 182
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Four Discrete Probability Distributions
OBJECTIVES:
a. Distinguish between discrete random variables and continuous random variables.
b. Construct a discrete probability distribution and its graph.
c. Determine if a distribution is a probability distribution.
d. Find the mean, variance, and standard deviation of a discrete probability distribution.
e. Find the expected value of a probability distribution.
f. Determine if a probability experiment is a binomial experiment.
g. Find binomial probabilities using the binomial probability formula, a binomial probability
table, and technology.
h. Construct a binomial distribution and its graph.
i. Find the mean, variance, and standard deviation of a binomial probability distribution.
j. Find probabilities using the geometric distribution.
k. Find probabilities using the Poisson distribution.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 4.1 Problems #1, 2, 5-8, 11, 12, 15-18, 21-28, 31, 32, 35, 38, 45, 47, 49
Pages 201 - 205
Sec. 4.2 Problems #1, 3, 7-9, 15-17, 22, 26, 27 pages 215 - 218
Sec. 4.3 Problems # 1, 2, 5, 6, 11-14, 17, 20-23, 25, 27 pages 226 - 228
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Five Normal Probability Distributions
OBJECTIVES:
a. Interpret graphs of normal probability distributions.
b. Find areas under a normal curve, and use them to find probabilities for random variables
with normal distributions.
c. Find and interpret standard z-scores and find the value of a variable when its standard score
is given.
d. Find areas under the standard normal curve and find areas under any normal curve using a
table.
e. Compare data from two normal distributions.
f. Find probabilities for normally distributed variables using a table and using technology.
g. Find a specific data entry of a normal distribution given the probability.
h. Find sampling distributions and verify their properties.
i. Interpret the Central Limit Theorem.
j. Apply the Central Limit Theorem to find the probability of a sample mean.
k. Decide when the normal distribution can approximate the binomial distribution.
l. Find the correction for continuity.
m. Use the normal distribution to approximate binomial probabilities.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 5.1 Problems # 1-12, 15-40, 43-62 pages 248 - 252
Sec. 5.2 Problems # 1-8, 13, 14, 17, 18, 21, 22, 27, 28, 31, 32 pages 256 - 260
Sec. 5.3 Problems # 1-4, 14-17, 25-41, 47 pages 266 - 268
Sec. 5.4 Problems # 1- 8, 10-14, 17, 21, 25-27, 29, 30, 33, 34, 41, 42
pages 278 - 283
Sec. 5.5 Problems # 1-6, 9-17, 21, 22, 26, 29 pages 291 – 294
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Six Confidence Intervals
OBJECTIVES:
a. Find a point estimate and a maximum error of estimate.
b. Construct and interpret confidence intervals for the population mean.
c. Determine the required minimum sample size when estimating .
d. Interpret the t-distribution and use a t-distribution table.
e. Construct confidence intervals when n < 30 and is unknown.
f. Find a sample proportion.
g. Construct a confidence interval for a population proportion.
h. Determine a minimum sample size when estimating a population proportion.
i. Interpret the chi-square distribution and use a chi-square distribution table.
j. Use the chi-square distribution to construct a confidence interval for the variance and
standard deviation.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework!
Complete the following assigned exercises at the end of each section.
Sec. 6.1 Problems #1-10, 15, 16, 19-24, 29, 30, 33, 34, 39-41,
43, 51, 53, 54, 60, 69 Pages 317 - 323
Sec. 6.2 Problems #1-6, 9, 10, 13-15, 18, 21, 22, 24, 27, 29 Pages 330 - 332
Sec. 6.3 Problems #1-6, 13-18, 21, 22, 27, 28a, 33 Pages 339 - 342
Sec, 6.4 Problems #1- 4, 8, 9, 22 Pages 348 - 350
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Seven Hypothesis Testing with One Sample
OBJECTIVES:
a. Identify the characteristics of a hypothesis test.
b. State the null hypothesis and the alternative hypothesis
c. Identify type I and type II errors and interpret the level of significance.
d. Determine when to use a one-tailed or a two-tailed statistical test.
e. Make a decision based on the results of a statistical test.
f. Write a claim for a hypothesis test.
g. Find critical values in a normal distribution.
h. Use the z-test to test a mean .
i. Find P-values and use them to test a mean .
j. Find critical values in a t-distribution.
k. use the t-test to test a mean .
l. Use technology to find P-values and use them to test a mean .
m. Use the z-test to test a population proportion p.
n. Find the critical values for a 2 - test.
o. Use the 2 - test to test a variance or a standard deviation.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework !
Complete the following assigned exercises at the end of each section.
Sec. 7.1 Problems #1-21, 23, 25, 29, 30 35, 36, 41, 42, 47, 49, 53, 54
Pages 375 - 378
Sec. 7.2 Problems #1-26, 29, 30, 33, 34, 39, 40 Pages 389 - 392
Sec. 7.3 Problems #1-8, 15, 16, 19, 20, 23, 24, 29, 37 Pages 403 - 406
Sec. 7.4 Problems #1-5, 9, 10, 13 Pages 411 - 412
Sec. 7.5 Problems #1-7, 9-11, 13-15 Pages 420 – 421
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Eight Hypothesis Testing with Two Samples
OBJECTIVES:
a. Identify the characteristics of two-sample hypothesis testing for the difference between two
population parameters.
b. Perform a two-sample z-test for the difference between two means, 1 and 2 using large
independent samples.
c. Perform a t-test for the difference between two population means, 1 and 2 using small
independent samples.
d. Decide whether two samples are independent or dependent.
e. Perform a t-test to test the mean of the differences for a population of paired data.
f. Perform a z-test for the difference between two population proportions p 1 and p 2 .
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework !
Complete the following assigned exercises at the end of each section.
Sec. 8.1 Problems #1-6, 13, 14, 17, 19, 20 35, 39 Pages 444 - 450
Sec. 8.2 Problems #1-5, 11, 13-15, 25 Pages 456 - 460
Sec. 8.3 Problems #1-4, 13, 14 Pages 466 - 468
Sec. 8.4 Problems #1-4, 7, 8, 25 Pages 475 - 478
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MAT 204 INTRODUCTION TO STATISTICS Fall 2009
CHAPTER OBJECTIVES - (Continued)
Chapter Nine Correlation and Regression
OBJECTIVES:
a. Describe linear correlation, independent and dependent variables, and the types of
correlation.
b. Find a correlation coefficient.
c. Perform a hypothesis test for a population correlation coefficient .
d. Find the equation of a regression line.
e. Predict y-values using a regression equation.
f. Interpret the three types of variation about a regression line.
g. Find and interpret the coefficient of determination.
h. Find and interpret the standard error of estimate for a regression line.
i. Construct and interpret a prediction interval for y.
j. Use technology to find a multiple regression equation.
k. Use a multiple regression equation to predict y-values.
HOMEWORK ASSIGNMENT:
NOTE: Work must be shown for each problem to receive full credit for your homework !
Complete the following assigned exercises at the end of each section.
Sec. 9.1 Problems #1, 2, 4, 5-8, 13-15, 17 Pages 507 - 508
Sec. 9.2 Problems #1-13, 18 Pages 517 - 519
Sec. 9.3 Problems #1-6, 13, 21 Pages 531 - 534
Sec. 9.4 Review the problems in the Student Solutions Manual. Pages 539 - 540
Chapter Ten Chi Square Tests and the F-Distribution
OBJECTIVES:
a. Use the chi-square distribution to test whether a frequency distribution fits a claimed
distribution.
b. Use a contingency table to find expected frequencies.
c. Use a chi-square distribution to test whether two variables are independent.
d. Interpret the F-distribution and use an F-table to find critical values.
e. Perform a two-sample F-test to compare two variances.
f. Use one-way analysis of variance to test claims involving three or more means.
g. Describe a two-way analysis of variance.
HOMEWORK ASSIGNMENT:
Sec. 10.1
Sec. 10.2
Sec. 10.3 TO BE ASSIGNED IN CLASS
Sec. 10.4
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