Download MATH 243 - Oregon Institute of Technology

Essential Studies Course Approval Form
Math 243 Introductory Statistics
Course Number & Title: _____________________________________________________________
(use a separate form for each course and ESLO)
I. Logistical Information: List the term(s) offered, locations and modes of offering, and projected capacity:
The Math 243 course is an introductory course for non-math-intensive majors, such as
Communication, Psychology, Dental Hygiene. This course will also satisfy part of the
Quantitative Literacy Essential Studies requirement. The course is offered every term both
online and on campus.
There will be an increase in demand for this course since currently the MIT majors are not
required to take a statistics course.
100ofis Achievement
a prerequisite. & Prerequisites
II.Math
Levels
What is this course’s level of achievement for the ESLO? (Select foundation, practice or capstone)
o Foundation. Learning new knowledge and skills. Assignments reflect significant scaffolding; highly structured
environment. Active learning is appropriate at this level.
o Practice. Learning how to apply knowledge and skills in scripted examples. Assignments reflect moderate
scaffolding, but students are learning how to work with less structured/open-ended problems and situations.
Prerequisite courses: _____________________________________________________
Indicate which type of course and specific prerequisites this course builds on:
o Essential Practice. Practice courses taught by content area experts.
o Program-Integrated. Practice courses that require demonstration of ESLOs within the major.
o ESSE. Cross-disciplinary experience that demonstrates synthesis of all ESLOs.
o Capstone. Students meet the criteria with minimal or no prompting. Assignments reflect no scaffolding;
students work independently in unstructured environments.
Prerequisite courses: _______________________________________________________
III. ESLO: Indicate which ESLO and criteria this course will fulfill.
 COM
 IA
 ER
 TW
 QL
 DP
 Purpose
 Audience
 Evidence
 Genre
 Style & delivery
 Visual
 Justification
 Identify
 Investigate
 Support
 Evaluate
 Conclude
 Theory
 Recognition
 Logic
 Judgment
 Achieve purpose
 Fulfill roles
 Communicate
 Reconcile
 Contribute
 Develop strategies
 Adjust
 Calculate
 Interpret
 Construct
 Apply in context
 Communicate
 Recognize
 Know
 Understand
 Apply
 Oral
 Written
 IA-H
 IA-SS
 IA-NS
a. How do students learn and practice the targeted ESLO within this course? Briefly describe how the course as
a whole addresses the criteria checked above for the targeted ESLO, including potential texts, instructional approaches,
and/or course materials. (Attach detailed syllabus that includes course outcomes.)
Calculation: Students in this course will calculate descriptive statistics as well as probabilities.
These are done by hand and using various technologies including a calculator and Minitab.
Interpretation: Students will interpret probabilities as they relate to different statistical tests.
They will read and interpret graphs. They will interpret the meaning of the slope of a calculated
linear regression. This is a short list of what the student will be interpreting.
Constructing Representations: Students will construct various graphs of the data by hand, using
calculators and software.
Applications in Context: Statistics is inherently applications in context. Students will be given
data sets and asked to infer with regards to these data sets.
Communications: The student will communicate their findings. Clear communication will also
be expected with regards to calculated statistics as they relate to parameters.
b. How do students demonstrate the appropriate level of proficiency in this ESLO? Briefly describe a significant
assignment(s) and/or student work appropriate for proficiency assessment in this ESLO, identifying how the
assignment(s) will require students to demonstrate each of the criteria checked above. (Attach assignment(s).)
Calculation: See Test 1: 3d, 4, 5c, 6a Test 2: 4, 7, 9,
Interpretation: Test 1:1e, 9e, 6b Test 3, 4,11
Construction Representations: Test 1: 4a,
Applications in Context: Test 2: 6d, 8, Test 3: 6, 7
Communication: Test 1, 1e, Test 2: 1b, 2b, 8 Test 3: 7
Department chair and dean signatures indicate proposal fits departmental and academic strategic plans and are willing to commit appropriate resources to support
the proposed course. In addition, the department chair commits to ensuring course outcome alignment over all sections, locations and modes of delivery.
____________________________________
Department Chair
____________________________________
Dean
If submitting this form in conjunction with CPC changes, please submit by including with your CPC submission. If you are submitting this
form only for Essential Studies course approval with no other changes, please submit to GEAC support [email protected] or OW145.
Math 243 Introductory Statistics
Winter 2016
M,W,R,F 10:00
Instructor:
Terri Torres
Office Hours:
Monday and Wednesday 1:00-3:00, Thursday 12:00 or by appointment
Office:
Telephone:
e-mail:
Boivin 178
(541) 885.1468
[email protected]
Text:
Statistics by Agresti, 3e
Calculator:
It is recommended that each student have a graphing calculator.
Course Information: Descriptive statistics, numerical and graphical presentation of data,
estimation and margin of error, hypothesis testing, correlation,
interpretation of statistical results.
Course Objectives:
•
•
•
•
•
•
•
Read and interpret statistical analysis presented in journal articles.
Create and interpret tables and graphs of data.
Compute and interpret numerical measures of data.
Demonstrate an understanding of the basics of probability.
Analyze normally distributed data.
Demonstrate an understanding of the basic concepts of correlation.
Demonstrate an understanding of estimation and hypothesis testing.
Homework/ Homework will be assigned and graded. Exam and quiz questions will be
Quizzes:
representative of the homework assigned. Quizzes will be given every Monday.
There will be no make-up quizzes.
Testing:
There will be three exams given on the following dates: January 27th,
February 17th and March 9th. A comprehensive final exam will be given
on Wednesday, March 16th from 10:00-12:00. There will be no make-up
exams. A student may always take the test before the assigned test day if
notification is given well in advance.
Attendance: It is expected that you will attend each class meeting. If an emergency forces you
to miss class you are still responsible for the material covered that day.
Code of Conduct: Students are expected to demonstrate their knowledge with honesty and
integrity. OIT considers academic dishonesty to be an unacceptable practice. Any student that
chooses to violate this policy with regards to this course will receive an automatic F for the
course. Use of electronic devices such as iPods or cell phones will not be allowed during tests.
Accommodation: If you feel you may need a course adaptation or academic accommodation
because of a disability, or if you might need special arrangements in case the room or building
must be evacuated, please contact Disability Services for assistance in verifying the need for
accommodations and developing accommodation strategies. You may call 541-885-1031 for
further assistance.
Disrupting the Academic Environment: Obstruction or disruption of teaching, research,
administration or authorized activities on institutionally owned or controlled property is strictly
prohibited by Oregon Tech’s code of student conduct and may result in disciplinary action.
Extra Credit: If any extra credit is offered it will be available to all students in the course and
will be offered before the end of the term. No credit will be given after the course is completed.
No extra credit will be given on an individual basis.
Grading:
Test 1
Test 2
Test 3
Quizzes
HW
Final Exam
Total
100 points
90-100%
100 points
80-89%
100 points
70-79%
50 points
65-69%
50 points 64 and below
200 points
600 points
A
B
C
D
F
Assignment expectations:
•
•
•
•
•
•
•
•
•
Show Work! Correct answers without work will receive no credit.
If you turn in work that is messy or difficult to read, that assignment will not be graded
and you will receive no credit for it.
Circle the answer for each problem.
Work on both sides of the paper is allowed.
After the homework set is finished, fold the paper in half, lengthwise, left over right.
If multiple pages are used, staple the pages.
Place your name, assignment and date on the top of the paper on the corner opposite
from the fold.
Place you homework on the table in the front of the class before class starts.
Late homework will not be graded.
Homework
number
Section
1
2
3
4
5
6
7
8
1.1
1.2
1.3
2.1
2.2
2.3
2.4
2.5
9
10
2.6
3.1
11
3.2
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
3.3
3.4
4.1
4.2
4.3
4.4
5.1
5.2
5.3
5.4
6.1
6.2
6.3
7.1
7.2
7.3
8.1
8.2
8.3
8.4
8.5
9.1
9.2
9.3
9.4
9.5
10.1
10.2
10.4
Topic
How can you investigate data?
We Learn about Populations and Samples
Computers in Statistics
Types of Data
Graphical Summaries
Center of Quantitative Data
Spread of Quantitative Data
How Can Measures of Position Describe
Spread?
Graphical Summaries Misused
Association Between Two Categorical
Variables
Association Between Two Quantitative
Variables
Outcome Prediction
Cautions in Analyzing Associations
Experiment vs. Observation
Sampling
Poor and Good Ways to Experiment
Other Ways to Perform Studies
Probability and Randomness
Finding Probabilities
Conditional Probabilities
Probability Rules
Outcomes and Their Probabilities
Normal
Binomial
Sampling Distribution
Sample Means vs. Population Means
Inference about a Population
Point and Interval Estimates
Confidence Interval for Proportion
Confidence Interval for Mean
Sample Size
Using Computers for Estimation
Steps for Significance Tests
Tests about Proportions
Tests about Means
Types of Errors
Limitations of Significance Tests
Comparison of Two Proportions
Comparison of Two Means
Dependent Samples
Assignment
(odd unless stated
otherwise)
1.1, 1.2
1.7, 1.9,1.11, 1.13
1.19
2.3, 2.5, 2.7, 2.8
2.11, 2.17, 2.25, 2.27
2.31-2.37, 2.43, 2.45
2.48, 2.49-2.55
2.63, 2.70, 2.71, 2.73,
2.83
2.87, 2.89
3.1-3.7
3.11, 3.13, 3.16
3.25-3.35
3.45-3.51
4.3-4.11
4.23-4.31
4.33-4.39
4.45-4.53
5.1-5.5, 5.8
5.15-5.23
5.31, 5.37, 5.39, 5.49
5.53-5.59
6.1-6.9
6.23, 6.27, 6.29
6.35, 6.39, 6.41, 6.43
7.7, 7.9, 7.10
7.15-7.23
8.1, 8.5, 8.6, 8.9
8.11-8.19
8.27-8.33
8.49, 8.51
9.1-9.7
9.11-9.19
9.29-9.33
9.43-9.47
9.52, 9.53, 9.55
10.1-10.5
10.15-10.19
10.47-10.49
MATH 243
Test 1
Fall 2013
1. In a University of Wisconsin study about alcohol abuse amongst students, 100 of the 40,858 members
of the student body in Madison were sampled and asked to complete a questionnaire. One question asked
was, “On how many days in the past week did you consume at least one alcoholic drink?”
a) Identify the population.
b) Identify the sample.
c) What is the response variable?
d) Is the response variable categorical or quantitative?
e) Of the 100 students 29 answer “zero” to this question. Does this mean that 29% of the entire
population of UW students would make this response? Explain.
f) Is the numerical summary of 29% a sample statistic or a population parameter?
2. Classify the variable as either discrete or continuous.
a)________________________The time it takes an athlete to run 100 meters.
b)________________________The number of calls received between 8 a.m. and 5 p.m.
by a technical support professional.
3. The heights (in inches) of 30 adult males are listed below. A frequency distribution show the
frequency and relative frequency using five classes.
70
67
69
72
71
71
71
70
68
Height (in inches)
67.0-68.4
68.5-69.9
70.0-71.4
71.5-72.9
73.0-74.4
70
74
67
69
69
73
73
68
74
Frequency
6
5
13
2
4
69
71
70
68
71
71
70
71
69
Relative Frequency
0.20
0.167
0.433
0.067
0.133
a) Identify the variable.
b) Is the variable ʺheightʺ continuous or discrete?
c) A height of 69 inches belongs to the class having what frequency?
d) What percentage of the 30 adult males had heights between 73 and 74.4 inches?
e) What proportion of the 30 adult males had heights less than 70 inches?
f) Which category of heights represents the mode?
71
72
68
4. The following data represent the number of grams of fat in various breakfast foods at
McDonaldʹs.
Egg McMuffin®
Sausage McMuffin®
Sausage McMuffin® with Egg
English Muffin 3
Bacon, Egg & Cheese Biscuit (Regular Size Biscuit)
Bacon, Egg & Cheese Biscuit (Large Size Biscuit)
Sausage Biscuit with Egg (Regular Size Biscuit)
Sausage Biscuit with Egg (Large Size Biscuit)
Sausage Biscuit (Regular Size Biscuit)
Sausage Biscuit (Large Size Biscuit)
Biscuit (Regular Size)
Biscuit (Large Size)
Bacon, Egg & Cheese McGriddles®
Sausage, Egg & Cheese McGriddles®
Sausage McGriddles®
Source: McDonaldʹs Corporation
a) Construct a dot plot for these data.
b) Use your calculator to calculate the mean.
c) Use your calculator to calculate the standard deviation.
d) Calculate the fine-number summary.
e) Are there any outliers?
12
22
27
3
25
30
32
37
27
31
11
16
21
32
22
5. According to the article ʺMotion Sickness in Public Road Transport: The Effect of Driver,
Route and Vehicleʺ, seat position within a bus may have some effect on whether one experiences
motion sickness. The table below classifies each person in a random sample of bus riders by the
location of his or her seat and whether nausea was reported.
Nausea
Front
Middle
Rear
Total
No
58
166
193
417
Nausea
870
1163
806
2839
Total
928
1329
999
3256
Source: Ergonomics (1999): 1646-1664.
a) What is the response variable?
b) What is the explanatory variable?
c) Calculate the conditional proportions for sitting in the rear of the bus.
Rear
d) What proportion of all sampled bus riders experienced nausea?
6. Based on findings from the Health and Nutrition Examination Survey conducted by the
National Center for Health Statistics from April 1971 to June 1974, the regression equation
predicting the average weight of a male aged 18-24 (y) based on his height (x) is given by
yˆ  172.63  4.842 x
a) Based on this equation, how much should a 72 inch tall man weigh?
b) What is the meaning of the slope in this situation?
7. A psychologist does an experiment to determine whether an outgoing person can be identified
by his or her handwriting. She claims that the correlation of 0.89 shows that there is a strong
causal relationship between personality type and handwriting. Explain what is wrong with her
interpretation.
8. A study shows that the amount of chocolate consumed in Canada and the number of
automobile accidents is positively related. What could be a potential lurking variable?
9. The heights of young women are symmetric with a mean of 64.5 inches and a standard
deviation of 2.5 inches.
a) Give an interval about which about 95% of the heights fall.
b) Would a height of 57 inches be considered unusual? Justify your answer.
10.
a) The shape of the distribution above is best described as_______________________.
b) With respect to the mean and median for the graph above, which of the following is most
likely?
i) mean < median
ii) mean > median
iii) mean = median
Math 243
Winter 2016
Test 2
1. You want to conduct and experiment with your class to see if students prefer Coke or Pepsi.
a) Explain how you could do this, incorporating ideas of blinding and randomization,
i) with a completely randomized design and
ii) with a matched pairs design.
b) Which design would you prefer and why?
2. A Rueters story reported that “The number of heart attacks victims fell by almost 60% at one
hospital six months after a smoke-free ordinance went into effect in the area of Helena, Montana,
a study showed, reinforcing concerns about second-hand smoke.” The number of hospital
admissions for heart attack dropped from just under seven per month to four a month during the
six months after the smoking ban.
a) Did this story describe an experiment or an observation?
b) In the context of this study, describe how you could explain to someone who has
never studied statistics that association does not imply causation. For instance, give a potential
reason that could explain this association.
3. A bottling company would like to estimate the proportion of its daily production (5000 cases)
that meets the appropriate filling guidelines. To do so, 5 cases a day are randomly are chosen and
all of the bottles within these corresponding 5 cases are checked against the guidelines. What
type of sampling was used here?
4. II. In the following probability distribution, the random variable X represents the number of
activities a parent of a student in grades 6 through 8 is involved in.
X
0
1
2
3
4
P(X= x) 0.073 0.117 0.258 0.322 0.230
a) What is the probability that a randomly selected student has a parent involved in three
activities?
b) What is the probability that a randomly selected student has a parent involved in three
or four activities?
c) What is the probability that a randomly selected student has a parent that is NOT
involved in zero activities?
5. A couple plans to have two children. Each child is equally likely to be a boy or girl, with sex
independent of that of the other child.
a) Construct a sample space for the genders of the two children. (List all the possible
combinations.)
b) Find the probability that both children are girls.
6. The primary aim of a study by Tasha Carter et al. was to investigate the effect of the age as
onset of bipolar disorder on the course of the illness. One of the variables investigated was
family history of mood disorders. The table below shows the frequency of a family history of
mood disorders in the two groups of interest (Early age at onset defined to be 18 years or
younger and Later age at onset defined to be later than 18 years).
Family history of disorders Early (E) Later (L) Total
28
35
63
Negative (A)
19
38
57
Bipolar Disorder (B)
41
44
85
Unipolar (C)
53
60
113
Multiple Disorders (D)
141
177
318
Total
Suppose we pick a person at random from this sample.
a) What is the probability that this person will be 18 years old or younger (E)?
b) What is the probably that the family history will be Unipolar (C) given that they are
Later (L)?
c) What is the probability that the person will be Early (E) given that family history is
Negative (A)?
d) Are the events Early (E) and Negative (A) independent? Justify your answer.
.
e) What is the probability that the individual is Later (L) or Negative (A)?
7. Let x denote the time it takes to run a road race. Suppose x is approximately normally
distributed with a mean of 190 minutes and a standard deviation of 21 minutes.
a) If a runner is selected at random what is the probability that the runner will complete this
road race in less than 150 minutes?
b) What is the probability that the runner will be between 205 to 245 minutes?
c) How fast would the runner need to be to qualify as the faster (lower) 7%?
d) Between what times will the middle 52% of the runner’s times be?
e) A group of 12 runners decide to race together. What is the probably that their average
score will be greater than 175 minutes?
f) How fast would the average of a group of 12 runners need to be eligible as the slowest
(highest) 4%?
8. A couple has five children, all girls. They are expecting a sixth child. The father tells a
friend that by the law of large numbers the chance of a boy is now much greater than ½.
Comment on the father’s statement.
9. In the United States 6% of the population eligible to donate blood actually do. If 15 people
are selected at random find the following:
a. the probability that exactly 5 of them will donate blood.
b. that greater than or equal to 3 of them will donate blood.
BONUS ( Do both.)
Of 346 items tested, 12 are found to be defective. Construct a 95% confidence interval to
estimate the proportion of all such items that are defective.
2. A researcher for a car insurance company wishes to estimate the mean annual premium that
women aged 25-30 pay for their car insurance. A random sample of 16 women aged between 25
and 30 yields the following annual premiums, in dollars.
582
748
594
856
658
662
723
610
466
777
580
720
941
704
725
985
Use the data to obtain a 99% confidence interval the mean annual premium for all women aged
between 25 and 30.
MATH 243
Test 3
Winter 2016
1. Professor Whata Guy surveyed of his Introduction to Statistics class of 420 students. One of the
questions was ʺWill you take another mathematics class?ʺ The results showed that 252 of the students
said yes.
a) What is the value of p̂ ?
b) Construct a 95% confidence interval for the population proportion.
2. Suppose a confidence interval for μ turns out to be (190, 250).
a) Calculate the sample mean.
b) Calculate the margin of error.
3. A researcher wants to conduct a study to precisely estimate the proportion of cats that are "leftpawed". She hopes to construct a 95% confidence interval that has a margin of error of 6%. How
many cats does she need to use in her sample? Use the results of an original study of pˆ  0.476 .
4. A jewelry designer claims that women have wrist breadths with a mean  equal to 5 cm. A SRS of
the wrist breadths of 14 OIT women has a mean of 5.07 cm with a sample standard deviation of 0.33
cm.
a) Calculate a 99% confidence interval for the mean breadth of OIT women.
b) Can a jeweler claim that OIT women have the same wrist breadth as the general population?
Justify your answer.
5. An engineer has designed an improved light bulb. The previous design had an average lifetime of
1200 hours. Using a sample of 2000 of these new bulbs, the average lifetime of this improved light
bulb is found to be 1201 hours. Although the difference is quite small, the effect was statistically
significant at the 0.05 level. Suppose that in fact, there is no difference between mean lifetimes of the
previous design and the new design. Which of the following statements is true?
a) A Type I error has been committed.
b) A Type II error has been committed.
c) No error has been committed.
6. Determine the null and alternative hypotheses.
a) In the past, the mean running time for a certain type of radio battery has been 9.6 hours. The
manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has changed as a result.
b) At one high school, the average amount of time tenth-graders spend watching television
each week is 21.6 hours. The principal introduces a campaign to encourage the students to
watch less television. One year later, the principal wants to perform a hypothesis test to
determine whether the average amount of time spent watching television per week has
decreased.
7. A journal article reports that 34% of American fathers take no responsibility for child care. A
researcher claims that the figure is higher for fathers in a particular town. A random sample of 233
fathers from this town yielded 96 who did not help with child care. Do the data provide sufficient
evidence to conclude that in this town the proportion is higher than 0.34? Use a 0.05 significance level.
α = 0.05
Ho: p = 0.34 Ha: p > 0.34.
Test statistic: z = 2.32.
P-Value = 0.0102
State your conclusion in terms of the null.
8. Decreasing the confidence level (say, from 95% to 85%) will cause the width of a typical
confidence interval to
a) increase.
b) decrease.
c) remain the same.
9. The p-value is
a)
the probability that the null hypothesis is true.
b)
the probability that the alternative hypothesis is true.
c)
the probability, when the null hypothesis is true, of obtaining a sample as extreme as (or
more extreme than) the observed sample.
d)
the probability, when the alternative hypothesis is true, of obtaining a sample as extreme
as (or more extreme than) the observed sample.
10. A bootstrap distribution, based on 1,000 bootstrap samples is provided. Use the distribution to
estimate a 90% confidence interval for the population mean. Explain how you arrived at your answer.
11. A study was conducted to compare the effectiveness of two weight loss strategies for obese
participants. The proportion of obese clients who lost at least 10% of their body weight was compared
for the two strategies. The resulting 98% confidence interval for p1  p2 is (-0.3, 0.09). Give an
interpretation of this confidence interval. Did the obese participants lose weight?
A researcher wishes to determine whether people with high blood pressure can reduce
their blood pressure by following a particular diet. Use the sample data below to construct a 99%
confidence interval for 1  2 where 1 and 2 represent the mean for the treatment group and the
control group respectively.
BONUS****
Treatment
n1 = 85
Group Control Group
n2 = 75
x1 = 189.1
x2 = 203.7
s1 = 38.7
s2 = 39.2