NIAGARA UNIVERSITY MATHEMATICS DEPARTMENT

MAT 102 ‑ INTRODUCTION TO STATISTICS‑ Fall 2006

                        Section A: MWF 10:10-11:05 VINI 212

                        Section B: MWF 12:20-1:15 VINI 112

 

Instructor: Dr. Marlo Brown

Office: 343 Dunleavy Hall

Email address: mbrown@niagara.edu

Office Phone Number: 286-8192

Office hours: TR 9:30-12, F 9-10 or by appointment. I am here to help you. Please see me as soon as you start to get confused. 

 

Course Website: http://purple.niagara.edu/mbrown/102.htm

 

Course Description:  A study of the basic terminology and methods of elementary statistics including organization of data, measures of central tendency and dispersion, sampling theory, estimation and testing of hypotheses.  Also includes an introduction to correlation and linear regression.

 

Method of Teaching:  A mixture of demonstrating/explaining by the instructor and practicing/questioning by the students.

 

Required Materials

1.                  Text: Interactive Statistics (2nd Edition) by Aliaga & Gunderson

2.                  Calculator: The T1-83 calculator is required for this course.

 

Note: We will be using both the Textbook and the calculator in class on a regular basis.  So it is very important that you come to every class prepared with your book and calculator. 

 

Topics covered:  chapters 1-11, 13.  See the schedule for details.

Course Objectives: By the end of the semester the students should be able to

Learning Objectives

Assessed

Department Goals
  1. Set up hypothesis tests.

a)      Describe Type I & Type II errors for given situations.

b)      Compute and interpret p-values

c)      Determine when a test to be statistically significant and explain what that means.

Exam 1

Final Exam.

Problem Solving

Content knowledge

 

 

 

 

 
  1. Get random Samples

a)      Identify biases in Sampling.

Exam 1

Final Project

Content knowledge

Communication

  1. Describe data pictorially.

a)      Histograms.

b)      Box & whisker plots

Exam 2

Final Exam

Content knowledge

4. Calculate & interpret descriptive Stats:

     a)    Mean.

c)      Median

d)      Mode.

e)      Standard Deviation

f)        Range

g)      IQR

Determine which of the above are affected by outliers.

Exam 2

Final Exam

Final Project

Problem Solving.

5.Calculate Continuous Probabilities

a)      Normal Distribution.

b)      Uniform Distribution.

Exam 2

Final Exam.

Problem Solving.

6.Calculate discrete probabilities

a)      Expected Value.

Exam 2

Final Exam.

Problem Solving

7.Construct & interpret CIs for

               a) Means.

             b) Proportions.

Exam 3

Final Exam

Final project.

Problem Solving

 

8.   Construct & Interpret Hypoth Tests for

    1. Means.
    2. Proportions
    3. Differences between means.

Exam 3

Final Exam

Final Project.

Problem Solving
  1. Calculate & interpret Bivariate Stats
    1. Regression Line:
    2. Correlation Coefficient.

Exam 3

Final Exam.

Problem Solving

 

10. Gather, analyze and interpret data:

  1. Summarize the results of the analysis.
  2. Recognize the population the results can be extended based on how the data was collected

Final project.

Communication

Technology

 

 

 

Grading policy:

  1. Quizzes: There will be announced and unannounced quizzes given approximately once a week.  Each quiz will be worth 10 points.  The lowest quiz grade will be dropped.   There will be no make-up quizzes given. 
  2. Homework will be given daily.   Periodically throughout the semester, homework will be collected and graded.  Each homework will be worth 10 points.  The lowest homework grade will be dropped.  No late homework will be accepted.  On all assignments, show all work.  Homework received without sufficient work shown will receive no credit. Your success in this course depends on the commitment you make to the daily assignments.
  3. Three (3) in class hour exams will be given.  Tentative dates and likely coverage.

Exam 1: Monday Sept 25, chapters 1-4.1:  assessing objectives 1-2

Exam 2: Wednesday Nov. 1, chapters 4.4-8: assessing objectives 3-6

Exam 3: Wednesday Dec. 6 chapters 9-11, 13:  assessing objectives 7-9

4.      Project: Each student should do a mini-research project.  Each student should collect and analyze data on two variables.  One variable must be quantitative and the other variable qualitative with two levels.  Students will test whether there is a difference between the two groups.  The project should be typed and should contain

a.       An introduction: What problem is being studied? What is the population? How was the data sampled?  Possible biases in the sample.

b.      Descriptive statistics on each variable: Mean, Median, mode, range, standard deviation, IQR.  Comments on the above. 

c.       95% confidence intervals for the mean of both variables.

d.      A hypothesis test of whether there was a difference between the mean of the two variables.  Report a p-value and explain your conclusion in non-technical terms.

e.       Conclusion: What does your analysis tell you?

Due Dates:

a.                   Project Proposal: This should contain an introduction to the problem that is being studied as well as a detailed description of how the data will be sampled: Due Monday Oct. 2

b.                  Midsemester report: This should contain a revised introduction as well as descriptive statistics for each variable.  Due: Monday Nov. 13.

c.                   Final Report: Due Friday Dec. 1.

  1. There will be a cumulative final given during final exam week.  The final exam is mandatory for anyone wanting to get a passing grade in this class.
  2. Attendance is expected for all classes.  If you are absent, it is YOUR responsibility to find out what was covered in class, to get the assignment and have it done for the next class.  
  3. Your grade will be determined as follows:

      Quizzes: 10% Homework: 10% Tests 15% each, Project: 10% Final: 25%. 

  1. Grades will be assigned numerically according to the following scheme:
    96-100 A+, 90-95 A, 88-89 A-, 85-87 B+, 80-84 B, 78-79 B-

75-77 C+,  70-74 C,  68-69 C-, 65-67 D+, 60-64 D, Below 60: F    

Getting Help:  In addition to seeking help during the instructor’s office hours, and attending the weekly review sessions, students are encouraged to take advantage of scheduled tutoring available from the Learning Center (Seton Hall), as well as assistance available on a drop-in basis in DUNL 342.

 

Students With Disabilities:  Students with documented disabilities who may need accommodations, who have any emergency medical information the instructor should know of, or who need special arrangements in the event of an evacuation, should make an appointment with the instructor as early as possible in the semester, preferably no later than the first week of the semester.  Students must also register with Diane Stoelting, Coordinator of Specialized Support Services (286-8076, ds@niagara.edu) in order to facilitate the provision of needed accommodations.

 

Counseling Services and Academic Support:  The strains and workload of student life can sometimes feel overwhelming and it is easy to lose perspective when faced with academic, social, and personal demands. The staff of the office of counseling services in the lower level of Seton Hall and the Academic Support staff in the Learning Center in Seton Hall are here to help students manage the stresses of university life.  All private consultations are confidential and free of charge.  Appointment can be scheduled by calling 286-8536 (Counseling) or 286-8072 (Office of Academic Support).

 

Policy on Academic Honesty  The integrity of an academic community necessitates the full and correct citation of ideas, methodologies, and research findings. In addition, each student can promote academic honesty by protecting his or her work from inappropriate use. Academic honesty is essential to ensure the validity of the grading system and to maintain a high standard of academic excellence.  The principle violations of academic honesty are cheating and plagiarism.

Cheating includes the unauthorized use of certain materials, information, or devices in writing examinations, or in preparing papers or other assignments. Any student who aids another student in such dishonesty is also guilty of cheating.  Other possible forms of cheating include submitting the same work in more than one class without permission

Plagiarism is the presentation of ideas, words, and opinions of someone else as one’s own work.  Paraphrased material, even if rendered in the student’s own words, must be attributed to the originator of the thought.
Please refer to the undergraduate catalogue for Niagara University’s policy on cheating, plagiarism, procedures and penalties.

 

Bibliography:

Triola, Maria. Elementary Statistics 4th edition.  The Benjamin/Cunning publication, 1989

            Freedman, Pisiani, and Purves Statistics third edition.  Nortan

and company. 1998

            Bluman, Alan. Elementary Statistics: A step by step

approach third edition.  McGraw Hill, 1997

                        Tentative Schedule

 

Date

Section

Material

M8/28/06

 

Introduction to course.

W8/30/06

1.3

Type 1 and Type 2 errors

F9/2/06

1.4.1

Decision rules

W9/6/06

1.4.2

Direction of the extreme; 2 sided tests

F9/8/06

1.4.3

p-values

M9/11/06

1.6

Significant vs. important

W9/13/06

Chapter 2

Sampling

F9/15/06

3

Experiments

M9/18/06

4.2

Types of variables.

W9/20/06

4.4.4

Histogram

F9/22/06

Review

Review

M9/25/06

Test

Test chapters 1-4.1

W9/27/06

4.6

Scatter plots

F9/29/06

5.2

Mean, Median, Mode.

M10/2/06

5.3

Range, IQR, box and whisker; project proposal due.

W10/4/06

5.3, 4

Standard Deviation, Transformations

F10/6/06

7.1

Introduction to probability

W10/11/06

6.2

Normal Distribution

F10/13/06

6.2

Normal Distribution

M10/16/06

6.3

Uniform Distribution

W10/18/06

6.4

Discrete Probability

F10/20/06

7.3

Expected Value

M10/23/06

8.2

Sampling Distribution for a proportion

W10/25/06

8.4

Sampling Distributions for a mean.

F10/27/06

9.3

Testing Hypothesis about a population proportion

M10/30/06

Review

Review

W11/1/06

Test

Test chapters 4-8

F11/3/06

9.3

Testing Hypothesis about a population proportion

M11/6/06

9.4

Confidence Intervals for a proportion

W11/8/06

9.6

Sample Size

F11/10/06

10.2

Hypothesis testing for a mean

M11/13/06

10.3

Confidence Intervals for a mean; mid semester report due

W11/15/06

10.5

Confidence Intervals and Hypothesis testing.

F11/17/06

13.2

Scatter plots

M11/20/06

11.3

Unpaired t-test.

M11/27/06

13.3

Regression

W11/29/06

13.7

Correlation

F12/1/06

 

Which test do I use? Project due.

M12/4/06

Review

Review

W12/6/06

Test

Test

F12/8/06

Review

Review

 

                                                            Homework:

 

Section

Problems

1.3

Page 67-68 (1-9) odd

1.4.1

Page 70-71 (17, 19, 21)

1.4.2

Page 73-74 (29, 30ab, 31ab, 32)

1.4.6

Page 69-75 (16, 31, 33, 35)

1.6

Pages 79-80 (45-51)

Chapter 2

Pages 97-98 (1- 11 odd ) pages 107 (13-17 odd)

Chapter 3

Page 155-157 (1-7 odd) pages 164-167 (9-15) odd

4.2

Pages 219-220 (1-5)

4.4.1

Pages 262 (31-37) odd

5.2

Pages 311-312 (1-8)

5.3

Pages 333-337 (11,12, 14-16, 19-21)

6.3.1

Pages 376-380 (7-23 odd

6.3.2

Page 387-389 (37-43) odd

6.4

Pages 394-395(47-53) omit 53d

7.4.1

Pages 427(10-14)

7.5.1

Pages 482-483 (51-57) odd

7.4.5

Pages 441-442 (21-25) odd

8.2

Pages 526-527 (1-13) odd

8.4

Pages 551-552 (20-25)

9.3

Page 580-583 (1, 4, 5, 7-10, 12-16)

9.4

Pages 595-597 (20-25, 29, 31)

9.5

Pages 601-602 (32-35)

10.2

Pages 634-636 (9-17)

10.3

Pages 647-650 (19-27) odd

10.5

Pages 653-655 (31-35)

11.4

Pages 713-714 (21-29) odd

13.2-13.3

Pages 821-822 (1-5) odd

13.7

Pages 858-864 (13, 15, 23, 27, 29, 31)

 

                                                            Answers to even numbered problems:

 

Chapter 1

16) a) .067       b) .4        c) .767

30a) left    b) a=.2; b=.4

32) a) left       c) .2      d) no.

48) a)You think the subject has ESP when they don’t.       b) You think the subject does not have ESP when they do.       c) 1/52       d) 0       e) 1

Chapter 4:

2)a)  and c) Quantitative discrete.   b) and d)  Quantitative continuous.  

Chapter 5

6) a) median.     b) mean.

8) a) mean=5.1 median=3  b) mean=9.61; median=12 c) mean=6.53; median=6

12) b) between 25% and 50%. c) $37,000.

16) a) s=4.48; IQR=8     b) s=4.12; IQR= 7      c) s=3.84; IQR=6

18) median=40; mean=45.

Chapter 6:

48) a) .05       b) .95

 50) a) .25        b) .6        c) skewed to the right.

Section 7.4

52) E(X)=1.6      54) E(X)=0    56) E(X)=39; E(Y)=37

Section 8.4

20) N(14,1)

22) a) N(28,1)      b) i) 27, 29  ii) 26, 30  iii) 25, 31      c) i) N(28, .5)     ii) 27.5, 28.5

24) b)i) N(-1,.2)      iii) .3085

Section 9.3

8) H0: p=.05 vs.  H1: p>.05   Z=2.56; p-value=.005, decision: reject H0.

Conclusion: Unemployment rate increased.

10) H0:p=.5 vs   H1: p>.5  Z=4.09; p-value=.00002118; reject H0;

More than 50% of students feel this behavior is important.

12) H0: p=.2 vs    H1: p<.2  Z=-3.67; p-value=.00012; reject H0;

Less than 20% of workers are willing to work fewer hours.

14) a) False; b) .66

16) a) .06; b) .94

 Section 9.4

20) a) (.313, .407)  c) same d) (.345, .375)

22) a) (.046, .0967) b) (.041, .1021) c) (b) is wider.

24) a) We only surveyed “telephone households” b) 81% c) (.783, .837) d) .027

Section 9.5

32) 665     34) 1844

Section 10.2

10) H0: m=70 vs   H1: m>70 T=2.5; p-value=.012, reject H0,  Average speed exceeds 70 mph.

12) H0: m=16 vs    H1: m<16 T=-.88; p-value = .19; do not reject Ho. 

The average fish width may be 16 lb.

14) yes; new p-value =.06

16) H0: m=0 vs  H1: m>0 T=2.11; p-value= .02; do not reject H0. They may be the same.

Section 10.5

32) a) 1; b) can’t tell; c) yes; d) 4

34) a) 1 b) no; c) no; d) yes.