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Statistics
Overview
A general statistics course, which includes understanding data, measures of central tendency, measures of variation, binomial distributions, normal distributions, correlation and regression, probability and sampling distributions, Central Limit Theorem, confidence intervals, estimates of population parameters and hypothesis testing. Interpretation and data analysis are emphasized.
PREREQUISITES: A grade of C or better in MAT 100 (Intermediate Algebra) or MAT 120 (Math Modeling for Liberal Arts) and placement above or successful completion of ENG 060 (Preparations for College Reading III). A student needs a thorough knowledge of Algebra, good reading skills and familiarity with the graphing calculator before entering this course.
Syllabus
MAT177-80 Semester
PROFESSOR: your name here
Office: ______________
Telephone: ###-###-####
E-mail: I do not open emails if I do not recognize the sender
IMPORTANT: In the subject line, write Stats, Your Name and Topic
(Ex: Statistics, Jim Bird, Ch.1 question)
Office Hours: by appointment or on Google+ hangouts
COURSE
DESCRIPTION: A general statistics course, which includes understanding data, measures of central tendency, measures of variation, binomial distributions, normal distributions, correlation and regression, probability and sampling distributions, Central Limit Theorem, confidence intervals, estimates of population parameters and hypothesis testing. Interpretation and data analysis are emphasized.
PREREQUISITES: A grade of C or better in MAT 100 (Intermediate Algebra) or MAT 120 (Math Modeling for Liberal Arts) and placement above or successful completion of ENG 060 (Preparations for College Reading III). A student needs a thorough knowledge of Algebra, good reading skills and familiarity with the graphing calculator before entering this course.
TEXT BUNDLE ISBN: 0321643933 from the Bedford bookstore (781-276-4211) includes:
- Elementary Statistics by Mario F. Triola, ELEVENTH edition, Pearson, Addison-Wesley, 2010 (White cover with windmills in a field)
- MyMathLab Student Access Code (More on MyMathLab below)
- Graphing Calculator Manual for TI-83/84 Plus, And TI-89 by Patricia Humphrey (we require a TI-83 or 84 Plus, NOT a TI-89)
The bundle sells for slightly more than a new text alone. If you buy a used text, you can buy a MyMathLab access code online separately with a credit card but it may end up costing more. The text and MyMathLab access code are required. The Access code allows you to read the text online as an e-book and is necessary for homework and quizzes.
CALCULATOR: A TI-83 or TI-84 Plus is required. It is used in all math courses starting with Intermediate Algebra. Calculator activities are an integral part of the course.
Students are solely responsible for using any other calculator, including the TI-89.
A TI-connectivity kit (cable and software) connects the calculator to your computer so you can copy the calculator screen onto a word document. You will need it for the projects. It comes with some of the calculators. If not, you can buy it separately from a store or visit http://www.education.ti.com/store. If you prefer not to buy it, you can use the ones in the Math labs (AR 214 in Bedford or Room 406B in Lowell City bldg.)
INTENSIVE VALUES: This course satisfies the Writing and the Computer Intensive Values.
ATTENDANCE: Attendance and active participation during the whole class period improves students’ chance of success. Students who nap, socialize or for any reason do not participate in class work will be marked absent. Habitual tardiness is discouraged. If the instructor is delayed, wait 15 minutes before leaving, to avoid being marked absent.
Students can access the course websites from home in order to do homework and keep track of syllabus adjustments especially test dates.
Students who miss more than a week of classes should call or email the instructor.
Winter Weather: A delayed opening means the College opens at 10AM. Look for school closings on Blackboard, TV, Radio or Call (781) 280-3200 or (978) 656-3200. Consider your safety and make your own decision about driving based on the road conditions in your area. Students are not penalized for absence due to inclement weather.
TEACHING PROCEDURE: In addition to class meetings, this course uses Course Compass with MyMathLab. Students use MyMathLab to do online assignments and they use the graphing calculator extensively, thus minimizing computations and maximizing focus on assumptions and interpretations of results. The instructor leads class discussions, lectures, demonstrates the use of the calculator, posts course materials and announcements, and evaluates students’ work. Students stay informed by attending class and by reading online announcements. Students’ efforts determine how well they learn. Students use their organizational skills to stay involved and meet all the deadlines. A pro-active attitude is necessary to stay organized, meet assignment deadlines and adjust to syllabus changes (if any) in a timely way.
CLASS ATMOSPHERE/ BEHAVIOR: An interactive, relaxed, and courteous atmosphere helps students achieve their full potential. Students are expected to focus on the subject matter and be mindful of the instructor and other students. Misconduct and disruptive behavior are not acceptable. Social conversations, swearing, moving around or going in and out of class or any other disruptions are not tolerated. A student who continues to disrupt the learning process will be referred to the Dean and may be expelled from class. See the Student Handbook for policies and procedures set by the college.
Cell phones have to be silenced and put away. No text messaging. Cell phones are not to be used as calculators. In case of emergency (ex. sick child), notify the instructor and put cell phone on vibrate mode.
CRITICAL THINKING: Students evaluate relevant facts, state questions, list assumptions, and determine appropriate statistical methods to analyze information. They collect and/or study data from different perspectives and in different contexts. They solve problems from a variety of disciplines such as education, business, economics, health and social science. Many text exercises are based on real data. Students justify their conclusions and list sources of bias.
Grading: Your grade for the course will be computed based upon the following weighting system.
| Weekly Classwork & Attendance | 15% |
| Lecture Notes | 15% |
| Homework | 20% |
| 5 Unit Tests | 30% |
| Final Project | 15% |
| Group Evaluation | 5% |
Plagiarism is a very serious offense. Any plagiarized work (copied, without quoting the source, in part or fully, (from another student, the internet, a magazine, a book, or any other source) will result in a grade of ZERO.
SUPPORT:
- Math Tutoring Centers: Free tutoring. Ask for the Statistics tutors’ hours. Not all tutors can help with Statistics. Bedford: AR214 781-280-3707. Lowell: 406B on the 4th floor of the City building 978-656-3368.
- CourseCompass/MyMathLab: www.coursecompass.com
- Click on ebook, Tools for success and Multimedia library.
- CourseCompass Technical Support:
(1) 1-800-677-6337 (Monday-Friday 8AM-8PM and Sunday 5PM- 12AM)
(2) Click on Help and send email using the Product Support e-mail form
- Online Tutoring Sun through Thurs 5PM-12AM. 1-800-877-3016 or Visit the Tutor Center's registration page to sign up for tutoring. When asked for a registration, provide your access code.
- Middlesex computer support: 978-656-3301 for help with questions related to College computer issues (NOT for CourseCompass or MyMathLab)
- Writing Labs: For help with project writing, AR 211 in Bedford and 406B in Lowell. Also, use the spell check function on your computer.
- study group Form a study group to help each other. Helping each other does not mean copying from each other. Cheating has severe consequences.
Course Objectives
The extensive use of the graphing calculator reduces the drudgery of computations and allows us to concentrate on analysis, assumptions, and methodology. Real data collected by students as well as data obtained by searching the web or looking at library sources are the basis of some projects. The projects increase in difficulty and sophistication as the semester progresses.
Producing Data
- Identify population and sample
- List different sampling methods and evaluate them.
- Explain under-coverage and non-response
- Recognize the effect of the wording of questions on the responses.
- Differentiate between an observational study and an experiment.
- Recognize bias due to confounding of explanatory variables with lurking variables
- Identify the factors (explanatory variables), treatments, response variables, and experimental units or subjects in an experiment.
- Explain placebo effect and double-blind experiments
Describing data
- Identify variables
- Describe data graphically and numerically
- Find outliers
- Discuss the effect of extreme values on the mean, the median, and the standard deviation.
- Make a decision about which measure of central tendency to use and support that decision.
- Define a density curve and give the area under it.
- Define a normal curve
- Find the area under a normal curve corresponding to a given interval on the horizontal axis and vice versa
Sampling Distributions and Probability
- Identify parameters and statistics
- Define sampling distribution
- Describe the bias and variability of a statistic in terms of the mean and spread of its sampling distribution.
- State the connection between variability and sample size.
- Define probability and list the probability rules
- Recognize when a problem involves a sample proportion or a sample mean
- Find the mean and standard deviation of the sampling distribution of or
- List the requirements needed for the normal to approximate the sampling distribution of.
- State the Central limit theorem and explain its significance
- Use the normal distribution to calculate probabilities that concern or
- State the law of large numbers
Confidence Intervals and Significance Tests
- State in non-technical language what is meant by statements of confidence such as “95% confident”.
- Find a confidence interval for a population mean for known or unknown σ and explain what it means
- Find a confidence interval for a population proportion and explain what it means.
- Recognize when you can safely use a confidence interval formula and when the sample design or a small sample from a skewed population makes it inaccurate.
- Explain the interconnection between sample size, level of confidence and margin of error
- Find the sample size required to obtain a confidence interval of specified margin of error when the confidence level is given.
- Explain the connection between confidence level, significance level, and critical values.
- State the null and alternative hypotheses in a testing situation when the parameter in question is a population mean or a population proportion p
- Explain in non-technical language the meaning of the P-value.
- Find the z statistic and the P-value
- Assess statistical significance at standard levels either by comparing P to
- Explain the connection between significance testing and the importance of an effect.
- List the assumptions behind hypothesis testing for a proportion and for a mean
- Recognize from the design of a study whether one-sample, matched pairs, or two-sample procedures are needed.
- Use the t procedure to obtain confidence intervals and to perform significance tests after checking for normality and for outliers.
- Use the z procedure to give a confidence interval for a population proportion p and to carry out significance tests.
Examining Relationships
- Identify the explanatory and the response variables
- Draw a scatter plot for two quantitative variables
- Compute the correlation coefficient r for quantitative variables
- Find the least-squares regression line and graph it
- Use r2 to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable.
- Recognize outliers and potentially influential observations
- Calculate the residuals and plot them. Recognize unusual patterns.
- Find possible lurking variables and explain how they might affect the conclusion
- Explain the difference between correlation and cause-and-effect
Chapter Lectures YouTube Playlist
Homework Problems YouTube Playlist
This is the YouTube Playlist URL for the homework problem videos I am creating
https://www.youtube.com/playlist?list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi
Chapter 1
1.3 - https://www.youtube.com/watch?v=3TPXLZ_DTTY&list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi&index=2&t=63s
1.15 - https://www.youtube.com/watch?v=l1a6cnwCGfc&list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi&index=3&t=0s
Chapter 2
2.1 - https://www.youtube.com/watch?v=T-okn19YWNE&list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi&index=4&t=0s
Chapter 4
2.11 - https://www.youtube.com/watch?v=asCUv6RKWpc&list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi&index=5&t=0s
2.16 - https://www.youtube.com/watch?v=-H1n8Hsp6Nc&list=PLlSSosOI1uj4IRzzOFFSnbYMzlnyqIqKi&index=5
Final Project
Statistics 177
Final Project
You will choose two different numerical variables from the data set, randomly select 60 countries, and analyze this information using the methods of descriptive and inferential statistics.
Section 1 –Analyze each of the two variables separately.
(40 POINTS)
Your project should include the following:
- An introduction explaining what two variables you want to explore using statistical methods. State the individuals and the two variables.
- A complete table of data.
- Frequency tables and histograms for the two distributions. A separate frequency table and histogram for each variable.
Discuss the choice of classes. How did you come up with it? How could choosing different classes change your histogram?
- Detailed descriptions of both histograms in words:
What is the shape of this distribution? What is the center? How much variation is in the data?
Are there any outliers?
- A stemplot for each variable.
- Detailed interpretation for each stemplot in words: range, mode(s), symmetry or skewness, outliers.
- Median, mean, and mode for each variable. For each of the two variables compare its mean, median and mode and comment on their differences and similarities. Give the standard deviation for each variable and explain its meaning.
- Use the range rule of thumb to estimate the standard deviation of each variable and compare this approximation with the values found in number 7.
- The five-number summary and a boxplot for each distribution. Give a detailed interpretation of each five-number summary in words.
Section 2 –Determine if there is correlation between your two variables.
(40 POINTS)
Using your data, you will explore possible connections between your two variables by completing the following.
- Make a scatterplot of all your data: one dot for each individual (60 dots). Label both axes clearly. Comment on your choice of the explanatory and response variables: which of the two variables you made explanatory and why.
- Regression line: its equation and graph together with the scatterplot.
- Correlation coefficient and its complete interpretation in words: sign, strength, what it means in terms of your specific variables.
- Coefficient of determination: its value, what it means in terms of your specific variables.
- Predictions made with the help of the regression line. Choose two different values of x and find what values of y you can predict for them; then choose two different values of y and find what values of x you can predict for them. Comment on reliability of these predictions in your particular case: use the value of correlation to estimate how reliable they are.
- Conclusion and Interpretation. Summarize your findings. Discuss possible outliers and influential points. Discuss possible errors involving lurking variables.
Section 3 –Determine if there is a difference between Global Income Groups.
(20 POINTS)
Using your data, you will determine if there is a difference between one of the variables you chose based upon the Income Groups the countries chosen belongs.
- State both the null and alternative hypotheses.
- State your choice of significance level and why you chose this level?
- Explain why or why not the null hypothesis was rejected. Use a p-value and F-value in your explanation.
- Write statements that explain what rejecting or not rejecting the null hypothesis means.
- What are your overall conclusions?