Download Probability and Statistics CPA

Mathematics Department
Probability and Statistics CPA
Course Syllabus
2015-2016
Instructor: Greg Aschoff
e-mail: [email protected]
Phone: 973-228-1200 X839
A. Grading Policy – course work will be graded as follows:
a. Summative Assessments (test, quizzes, projects) – 90% of grade
b. Formative Assessments (homework) – 10% of grade
c. All grades should be verified in genesis on a regular basis
B. Classroom
a. Rules of Conduct
i. Follow all rules as stated in student handbook
ii. Come prepared to class with all required materials
iii. No food or drinks in classroom
iv. No cell phone use in class
b. Required Material
i. Textbook
ii. Pencils
iii. Graphing calculator
iv. Three ring binder
c. Homework
i. All homework will be posted on the teacher’s school website
ii. Homework will not be accepted late unless the student has
been absent and/or has a medical excuse
iii. Missed homework should be made-up for understanding of
concepts
d. After School Help
i. Available Tuesdays, Wednesdays, Thursdays
ii. Will notify students if I cannot stay on a particular day
e. Attendance
i. Follow all rules as stated in student handbook
ii. One day to make up work for every day absent
iii. Work assigned prior to absence(s) will be due on the first day
back
f. Academic Integrity
i. Students are to hand-in their own work
1. Receiving assistance is different from copying
ii. Cheating will result in a zero on the assessment and a call
home to the parent
C. Course Description: Probability and Statistics CPA covers four major
domains in a problem-based environment. The topics of the course are
divided into four major themes: exploratory analysis, planning and
conducting a study, probability, and statistical inference. Using real world
data and authentic problems, the course utilizes various technologies,
including the graphing calculator and computer, in facilitating teaching and
learning. Students do a significant amount of reading and writing in
learning the major concepts and tools for collecting, analyzing, and drawing
conclusions from data.
D. Course Objectives: This course has been designed with respect to and in
compliance with the expectations set forth in the New Jersey Common
Core State Standard. The course’s objective is to use inductive and
deductive reasoning to analyze, observe, and problem solve in order to
answer the following essential questions based on the Common Core State
Standard Student Learning Objectives :
A. Displaying Distributions with Graphs
1. Variables – categorical vs. quantitative
2. Graphs - histogram, stemplot, boxplot, bar graph
B. Describing Distributions with Numbers
1. Measuring center: mean, median, mode
2. Measuring spread: range, quartiles, interquartile range (IQR), standard deviation, variance
3. Describe shapes of distributions
A. Density Curves and the Normal Distributions
1. Density curves
2. Shape of normal curves and 68-95-99.7 empirical rule
3. Calculate percentiles
B. Standard Normal Calculations
1. z-scores
2. Standard normal distribution & calculations
3. Find normal proportions and find a value given a proportion
4. Assess normality: normal probability plots
A. Scatterplots
1. Response vs. explanatory variables
2. Interpreting scatterplots
B. Correlation
1. Calculate r
2. Facts about correlation
C. Least-Squares Regression Line (LSRL)
1. LSRL – equation (slope, intercept)
2. Facts about the LSRL
3. r2 in regression – coefficient of determination
4. Residuals, residual plots, interpretation of plots
5. Outliers and influential observations in regression
A. Transforming to Achieve Linearity
1. Settings in which a transformation is necessary to achieve linearity
2. Transformations involving powers and logarithms to linearize curved relationships.
B. Relations between Categorical Variables
1. Two way tables
2. Marginal and Conditional Distributions
3. Simpson’s Paradox
C. Establishing Causation
1. Lurking Variables
2. Associations: Causation, Common Response, Confounding
A. Designing Samples
1. Simple random, stratified, cluster and multistage samples
2. Cautions about sample surveys and types of bias
B. Designing Experiments
1. Observational study vs. experiment
2. Experimental units, subjects, treatment, factors, levels
3. Comparative and completely randomized experiments
4. Logic and principles of experimental design – statistical significance
5. Cautions about experimentation
6. Block Design, Matched-Pairs Design, Double-Blind
A. Simulation
1. Simulation Basics
2. Simulations with the Calculator, Computer, Table of Random Digits
B. Probability Models
1. Idea and language of probability
2. Sample space, events, outcomes, multiplication principle
3. Independent Events
4. Disjoint Events
5. Venn diagrams and tree diagrams
C. General Probability Rules
1. General Addition Rules
2. General Multiplication Rules
3. Conditional probability
A. Discrete and Continuous Random Variables
1. Probability distributions and probability histograms for discrete
2. Normal distributions as probability distributions for continuous
B. Means and Variances for Random Variables
1. Mean and expected value for discrete random variable
2. Law of large numbers
3. Rules for means and variances
A. The Binomial Distribution
1. Conditions that need to be present to have a binomial setting
2. Calculate binomial probabilities using binomial formula and calculator
3. Mean and variance of a binomial distribution
B. The Geometric Distribution
1. Conditions that need to be present to have a geometric setting
2. Rules for calculating geometric probabilities
3. Mean and variance of a geometric distribution
A. Sampling Distributions
1. Parameter vs. statistic
2. Sampling variability
3. Unbiased estimator
B. Sample Proportions
1. Sampling distribution of a sample proportion
2. Compute the mean and standard deviation for the sampling distribution of pˆ
3. Using the normal approximation for pˆ
C. Sample Means
1. The mean and standard deviation of the sampling distribution of a sample mean
2. The central limit theorem
A. Confidence Intervals: The Basics
1. Statistical confidence
2. Critical values and confidence level
3. Conditions to construct a confidence interval
4. Margin of error
B. Confidence interval for a population mean
C. Confidence interval for a population proportion
A. Significance Tests: The Basics
1. Reasoning of a significance test
2. Stating Hypotheses
3. P-value, significance level, and statistical significance
4. Conditions to perform a significance test
B. Carrying Out Significance Tests
1. z Test for a population mean
2. Relationship between a two-sided significance test and a confidence interval
C. Use and Abuse of Tests
1. Statistical significance vs. practical importance
D. Using Inference to Make Decisions
1. Type I and II errors
2. Error probabilities
3. Power
A. Tests about a Population Mean
1. Standard error, degrees of freedom,
t -distributions
2.One-sample t -significance test for a population mean
3. Paired t- test
B. Tests about a Population Proportion
1. Significance test for a population proportion
A. Comparing Two Means
1. Conditions necessary for doing inference involving two population means
2. Two-sample t- procedures
3. Construct a confidence interval for the difference between two population means
4. Conduct a significance test for the difference between two population means
B. Comparing Two Proportions
1. Mean and standard deviation of the sampling distribution
2. How the standard error differs between constructing a confidence interval and conducting a significance te
3. Conditions necessary for doing inference involving two population proportions
4. Construct a confidence interval for the difference between two population proportions
5. Conduct a significance test for the difference between two population proportions
A. Test for Goodness of Fit
B. Inference for Two-Way Tables
1. Chi-square test of association/independence
2. Chi-square test for homogeneity of populations
1. Conditions necessary to do inference for regression
2. Standard error about the least-squares line
3. Confidence interval for the slope of the regression line
4. Significance test for the slope of the regression line
E. TEXTS/RESOURCES
Statistics: Informed Decisions Using Data, Third Edition. Michael Sullivan, © 2010