Santa Monica College
Page 11 of 11
Santa Monica College
Mathematics Department Addendum
Math 54 – Elementary Statistics
Prerequisite Comparison Sheet – exit skills of Math 18/20 and entry skills for Math 54
Exit Skills for Math 18Upon successful completion of Math 18, the student will be able to:
A. / Solve linear inequalities in one and two variables, graph their solution sets, and express the answer in interval notation where appropriate..
B. / Solve literal equations for a designated variable.
C. / Solve linear, quadratic, exponential and logarithmic equations.
D. / Solve systems of linear equations using matrix row reduction
E. / Graph the solution sets of systems of linear inequalities.
F. / Given its graph, determine whether a relation is a function and whether it is one-to-one, and determine its intercepts and domain and range.
G. / Graph and determine the domain and range of linear, quadratic, exponential and logarithmic functions.
H. / Use proper mathematical notation to evaluate functions and obtain their inverses
I. / Evaluate simple expressions involving summation notation.
J. / Determine terms of arithmetic and geometric sequences, and evaluate those series using relevant formulas.
K. / Set up and solve practical applications of the algebraic material.
:
Exit Skills for Math 20 /Upon successful completion of Math 18, the student will be able to:
A. / Simplify advanced numerical and algebraic expressions involving multiple operations.
B. / Solve linear, quadratic, rational and absolute value inequalities, graph their solution sets, and express the answer in interval notation.
C. / Solve literal equations for a designated variable.
D. / Apply algorithms of completing the square, rationalizing the denominator, and long division and synthetic division of polynomials.
E. / Solve linear, quadratic form, simple cubic, radical, rational, absolute value, elementary exponential, and elementary logarithmic equations.
F. / Solve systems of linear equations in three variables using matrix row reduction.
G. / Graph the solution sets of systems of linear and quadratic inequalities.
H. / Perform operations on complex numbers.
I. / Perform operations on functions including composition of two functions and determine the domain of the resulting function.
J. / Use proper mathematical notation to evaluate functions and obtain their inverses.
K. / State and apply the fundamental properties of exponents and logarithms.
L. / Demonstrate knowledge of standard vocabulary associated with graphing, including but not limited to slopes of lines, intercepts, vertex of parabola, asymptotes, and interplay between graph and functional notation.
M. / Given its graph, determine whether a relation is a function and whether it is one-to-one, and determine its intercepts and domain and range.
N. / Graph using horizontal and vertical translations and determine the domain and range of linear, quadratic, simple cubic, radical, reciprocal, absolute value, exponential and logarithmic functions.
O. / Graph circles and parabolas using horizontal and vertical translation.
P. / Evaluate simple expressions involving summation notation.
Q. / Set up and solve practical applications of the algebraic material.
Entry Skills for Math 54 /
Prior to enrolling in Math 54 students should be able to
1. / Solve linear equations.
.2. / Evaluate complex numerical expressions (order of operations)
3. / Plot and interpret points on the Cartesian coordinate system.
4. / Plot linear equations using slope-intercept method.
5. / Translate verbally stated problems in to appropriate mathematical forms
6. / Solve linear equations and inequalities in a single variable.
7. / Evaluate an exponential function.
8. / Evaluate simple expressions involving sigma notation.
9. / Solve literal equations for a designated variable
10. / Given the description of a line, write the equation of the line
11. / Express the solution to an inequality using interval notation.
12. / Read information from a diagram or graph
13. / Calculate percents
14. / Calculate the area of a rectangular region
Santa Monica College
Student Learning Outcomes
Date: Fall 2009
Course Name and Number: Math 54 Elementary Statistics
Student Learning Outcome(s):
· Individual faculty members will develop and report on assessments for SLOs.
1. / Given a data set, students will analyze the data set and design a presentation of the information using tables, graphs and statistical calculations.2. / Given sample data, students will decide on and use appropriate estimation strategies to make inferences about the important characteristics of population data, including the mean, proportion and variation.
3. / Given sample data, students will decide on and use an appropriate test to reach conclusions about a hypothesis made about a population parameter.
Demonstrate how this course supports/maps to at least one program and one institutional learning outcome. Please include all that apply:
1. / Program Outcome(s):The student will demonstrate an appreciation and understanding of mathematics in order to develop creative and logical solutions to various abstract and practical problems.
As a result of learning about the methods of descriptive and inferential statistics, students will analyze and solve abstract and practical problems.
2. / Institutional Outcome(s):
As a result of studying instructor feedback given during lecture, or written on homework and exams, students will evaluate information critically and present solutions in a clear and logical manner.
Textbook: Agresti, A and Franklin, C, Statistics: The Art and Science of Learning from Data 2nd ed, Pearson Prentice Hall, 2nd edition
A Sample Schedule for Math 53
This schedule assumes a standard meeting schedule of 2hr 5min with 2 class meetings per week.
Session / Text Section/Activity /1 / Class Introduction
1.1-1.3 Statistics Overview
2.1 Data Types and Designs of Experiments
2 / 2.2 Statistical Graphs and Their Summaries
2.3 Center of Quantitative Data
3 / 2.4 Spread of Quantitative Data
2.5 Measures of Position
4 / 2.5 Measures of Position
2.6 How Graphical Summaries Can be Misused
5 / 4.1 Types of Studies: Experimental and Observational
4.2 Sampling Methods
4.3 Elements of a Good Experiment
4.4 Sample Surveys: Other Random Sampling Designs
6 / 3.1 Association Between Two Categorical Variables
3.2 Association Between Two Quantitative Variables
7 / Exam 1 - Over Chapters 1, 2, and 4
8 / 3.3 The Regression Line
3.4 Cautions in Analyzing Associations
9 / 5.1-5.2 Probability Fundamentals
10 / 6.1 Probability Distributions for Discrete Random Variables
6.2 The Normal Distribution
11 / 6.3 The Binominal Distribution
12 / 7.1 Sampling Distributions
7.2 The Mean and Standard Error of
13 / 7.3 The Central Limit Theorem
14 / 8.1 Point and Confidence Interval Estimates
8.2 Confidence Interval Estimates : Population Proportion
15 / Exam 2 – Over Chapters 3, 5, 6 , and 7
16 / 8.3 Confidence Interval Estimates : Population Mean
8.4 Choosing Sample Sizes
17 / 8.5 Bootstrap Methods
18 / 9.1 Intro to Hypothesis Testing
19 / 9.2 Hypothesis Testing about Proportions
9.3 Hypothesis Testing about Means
20 / 9.3 Hypothesis Testing about Means (continued)
9.4 Type I and Type II Error
9.5 Limitations of Significance Tests
21 / 10.1 Confidence Intervals :Two Population Proportions
10.2 Confidence Intervals :Two Population Means
22 / 10.3 Other Ways of Comparing Means and Proportions
10.4 Analysis of Dependent Samples
10.5 Statistical Control
23 / 11.1 Independence and Association
11.2 Chi-Squared Distribution
24 / 11.3 Measures of Association
11.4 Residual Analysis
25 / 12.1 Regression Analysis
12.2 Strength of Linear Association
26 / Exam 3 – Chapters 8, 9, 10, 11
27 / 12.3 Inferences about Association
12.4 Data Variation and the Regression Line
28 / 14.1 One-Way ANOVA
29 / Review Day
30 / Comprehensive Final Exam
SAMPLE Statistics Projects
Project #1
For this project, you will work in pairs on an assigned topic. What you turn in will be a report on your topic. Your report should be typed and should use clear concise English. You may present graphs or charts in the body of your report but put your data in an appendix. Be sure to cite any sources you used, including stores for data collection. If you are surveying, describe your sampling method and target population as well as any biases inherent in your sample. There is no required length to the project, simply complete the assignment to the best of your ability. Feel free to discuss your progress with me or submit work early for feedback.
1. Go to a local grocery store and collect data for at least 20 different soups from each of two major soup makers: for example, Campbell’s & Progresso. For each of the soups, record the per-serving amounts of calories, fat, and sodium. Summarize your data using any descriptive means you see fit. Provide a written conclusion about the similarities and differences between the brands.
2. Go to a large bookstore that has a prominent display of best selling fiction and nonfiction hardcover books. For each of these two categories find at least 20 books, graph your data using a scatter plot, and use these data to calculate the regression line for that category with price the dependent variable and the number of pages the independent or explanatory variable. How good is your line? Are there any apparent outliers in your data?
3. Go to the campus bookstore and select 30 new hardcover textbooks (be sure to describe how you choose your sample). For each book, record the number of pages and the price. Graph your data using a scatter plot, and use these data to calculate the regression line for that category with price the dependent variable and the number of pages the independent or explanatory variable. How good is your line? Are there any apparent outliers in your data?
4. Find a local real estate office that will let you browse the multiple listing service (MLS) for houses that are for sale in your neighborhood. Use a random sample of at least 50 houses and get the list price and square footage for each. Graph your data using a scatter plot, and use these data to calculate the regression line for that category with price the dependent variable and the square footage the independent or explanatory variable. How good is your line? Are there any apparent outliers in your data?
5. Go to a local grocery store and collect these data for at least 75 breakfast cereals: name, grams of sugar per serving, and shelf location (bottom, middle, or top). Group the data by cereal location and use three box plots to compare sugar content by shelf location. Comment on your finding
6. Anchoring effects: Research the “anchoring effect”. Ask a random sample of people to estimate 8x7x6x5x4x3x2x1 vs 1x2x3x4x5x6x7x8 for another sample. Summarize your results including 5 number summaries and means. Does the anchoring effect seem to hold?
7. Anchoring effects: Research the “anchoring effect”. Try the anchoring effect on the population of Kenya using a low anchor and a high anchor. Summarize your results including 5 number summaries and means. Does the anchoring effect seem to hold?
8. Choose two major grocery stores and try to determine which has the lower prices on a sample of 30 commonly purchased items. Explain your sampling procedure, display data appropriately, and write up conclusions.
9. Ask 50 randomly selected people the following question: “If you guess the next flip of a coin correctly you will win $100. The last four flips have been heads. What would you choose?” Display your results and explain the difference between the false “Law of Averages” and regression to the mean.
10. Who works more? Ask a random sample of 50 students the following question: “how many hours a week do you spend on school related work - for example going to class, doing HW, attending study sessions …?” Ask a random sample of at least 25 teachers, the same question (including teaching, preparing lectures, grading papers, going to meetings, office hours …). Prior to collecting the data, make a prediction. Summarize your results.
11. Complete a statistical analysis of ice cream. Compare one premium brand (Ben & Jerry’s, Hagen-Daz …) to a generic brand. How much more is the customer paying? What, besides taste are they getting? Check all ingredients & justify your conclusions with data.
12. Complete an analysis of sodas. Choose at least 25 regular sodas (not diet) at a grocery and compare grams of sugar per serving as well as price per ounce and any other quantities you find interesting. Display data appropriately and draw conclusions.
13. Loaded questions: pick a controversial question that is of interest to you. Write the question in three ways, survey at least 40 people for each question and summarize and comment on your results. Below is a sample. Describe your sampling process.
14. Research the “primacy effect”. Explain the effect in your own words. Come up with a survey to test this effect. Give multiple versions of the survey to different groups and report on your results.
15. Ask a random sample of at least 50 college students the following questions:
i. Do you think voting is important?
ii. Are you registered to vote?
Find out what percentage of college students are registered Los Angeles. Display your results and discuss any differences between what people say they do and what they actually do.
16. Conduct a small survey outside a public place (supermarket, video store …). The survey doesn’t matter here, but the catch is that you must do it twice. The first time, wear ordinary clothing (t-shirt, shorts, jeans). The second time dress up. Keep track of the percentage of people who are willing to respond to your survey and their characteristics. (One person can give the survey while the other can discretely take notes.)
17. Response Bias
The Project: You will design and conduct an experiment to investigate the effects of response bias in surveys. You may choose the topic for your surveys, but you must design your experiment so that it can answer at least one of the following questions:
-Can the wording of a question create response bias?
-Do the characteristics of the interviewer create response bias?
-Does anonymity change the responses to sensitive questions?
Write up:
A. Introduction: What form of response bias were you investigating? Why did you choose the topic you chose for the survey?