# Course Syllabus MATH 110 Introduction to Statistics 3 credits

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1 Course Syllabus MATH 110 Introduction to Statistics 3 credits Prerequisites: Algebra proficiency is required, as demonstrated by successful completion of high school algebra, by completion of a college algebra course, or their equivalent as determined by Portage staff. Instructor: Matthew Dodd, MS; H. Elaine Frey, MA Contact Info: Faculty may be contacted through the Portage messaging system Course web site address: Course meeting times: MATH 110 is offered continuously Course Description: A general introduction to mathematical statistics as a tool used in the decision making process. The course text, homework assignments and examinations will emphasize interpretation of data. The framework of the course is designed to develop in the student an understanding of summarized data (ungrouped and grouped) in both descriptive and inferential statistical applications through the use of frequency distributions, measures of central tendency and measures of dispersion; outcome probabilities and the various concepts related to discrete and continuous probability distributions; the concepts surrounding random sampling and interval estimating for populations and large & small samples; classical hypothesis testing and with one-tailed & two-tailed testing; comparisons involving means; regression analysis, and statistical process control methods. Course Outcomes: As a result of this course experience a student should be able to explain: The difference between qualitative and quantitative data, be able to organize the data and present a meaningful overview of the data through the use of frequency distributions, measures of central tendency (i.e. the mean, median and mode) and measures of dispersion (i.e. the variance, standard deviation and coefficient of variation) The rules involved in developing outcome probabilities and how to apply the appropriate counting methods in the development of the probabilities of outcomes in an experiment. The difference between a discrete probability distribution and a continuous probability distribution. The concepts involving random sampling, the sampling distributions of x-bar (x ) and p-bar (p ) and other methods. The null & alternative hypothesis in classical hypothesis testing along with type I and II errors; onetailed & two-tailed testing involving populations and both large & small samples. Linear regression analysis and lines of best fit. Each of these MATH 101 student learning outcomes is measured: Directly by: (1) module application problems (with instructor feedback) (2) exams (3) comparison of pre-course / final exam results

3 Grading Rubric: Module 1 Exam = 30 pts. Module 2 Exam = Module 3 Exam = Module 4 Exam = Module 5 Exam = Module 6 Exam = Module 7 Exam = Module 8 Exam = Module 9 Exam = 35 pts. Module 10 Exam = Final exam = 200 pts. Total 30 pts. 35 pts. 100 pts. 565 pts. The current course grade and progress is continuously displayed on the student desktop. Grading Scale: 89.5% - 100% ( pts) = A 79.5% % ( pts) = B 69.5% % ( pts) = C 59.5% % ( pts) = D <59.4% (<336 pts) = F Modules and Assignments Module 1: Module 2: An introduction to data and statistics. This module discusses why statistics are important, and where statistical analysis is used. Students will learn about different types of data that might be used in statistical analysis. Topics covered include: Quantitative and Qualitative Data, Experimental and Observational Studies, Data Errors, Outliers, Descriptive Statistics, Histograms, Populations, and Samples. An introduction to descriptive statistics using tabular, graphical and numerical methods. This module considers ways to describe and represent data. Topics covered include: Frequency Distributions, Relative Frequencies, Charts (Column, Bar, and Pie), Cross-Tabulation, Scatter Diagrams, Measures of Central Tendency, Percentiles, Quartiles, Measures of Dispersion, Z- scores, Bell Curves, and Sample Covariance. Module 3: An overview of probability. This module considers experiments and the likelihood that an event will occur. Students are taught to calculate probabilities using multiple techniques. Topics

4 covered include: Probability Distributions, Sample Space, Counting Techniques, Permutations, Combinations, Complements, Union, Intersection, Mutually Exclusive Events, Conditional Probabilities, and Bayes Theorem. Module 4: An introduction to probability distributions. Students will learn about the standard normal probability distribution, and how the data is distributed with respect to the mean. Topics covered include: Random Variables (Discrete and Continuous), Expected Values, Binomial Probability Distributions, Normal Distributions, and The Standard Normal Table. Module 5: An overview of sampling and sampling distributions. This module explains how to calculate descriptive statistics when working with a sample instead of the entire population. Topics Covered include: Statistical Inference, Simple Random Samples, Sample Mean, Sample Proportions, The Central Limit Theorem, Sample Error, and Sample Size. Module 6: An introduction to interval estimation. In this module students will learn how to take a sample, find its mean, and use this information to estimate the population mean. Students will be able to construct confidence intervals for the population mean. Topics covered include: Confidence Intervals, Confidence Levels, Means, and Proportions. Module 7: An introduction to hypothesis testing. In this module students will be guided through the process of hypothesis testing. Students will learn to make assumptions about a certain characteristic of the population and then test to see if the hypothesis is true. Topics covered include: Null Hypothesis, Alternate Hypothesis, One-Tailed and Two-Tailed Tests, Type I and Type 2 errors, and Level of Significance. Module 8: An introduction to comparisons involving means and proportions. In this module students will study interval estimation and hypothesis testing for differences between two population means as well as for differences between two population proportions. Topics covered include: Dependent Samples, Independent Samples, Hypothesis Testing Involving Differences between Means, and Hypothesis Testing for Dependent Samples. Module 9: An introduction to regression analysis. Students will learn how to calculate the linear correlation coefficient for a set of data to reveal how well two variables are correlated. Students will also learn how to find the best fit line that approximates the relationship between these variables. Topics covered include: Linear Correlation Coefficients, Positive Correlations, Negative Correlations, Critical Values Correlation Coefficient, and Linear Regression

5 Module 10: An overview of various tests that were not covered in previous modules. Students will learn about goodness of fit tests, tests for independence, and analysis of variance. Topics covered include: Chi-Square Distributions, F Distributions, Multinomial Experiments, Expected Counts, Goodness of Fit Tests, and Tests for Independence. Holidays: During the following holidays, all administrative and instructional functions are suspended, including the grading of exams and issuance of transcripts. New Year's Day Easter Memorial Day Independence Day Labor Day Thanksgiving weekend Christmas Break (one week before Christmas through New Year's Day) The schedule of holidays for the current calendar year may be found under the Student Services menu at Additional Tools A built-in scientific calculator for the course has been incorporated into the website and can be found in the tool bar above each module and exam page. If you choose to purchase a calculator, keep in mind that you do not need to purchase an expensive calculator as the features you will need are available on basic scientific calculators with a cost of less than \$20. Many mobile phones also include a scientific calculator and you may use a calculator during any exam.

6 Suggested Timed Course Schedule (to complete the course within a typical college semester) All Portage courses are offered asynchronously with no required schedule to better fit the normal routine of adult students, but the schedule below is suggested to allow a student to complete the course within a typical college semester. Despite this suggestion, the students may feel free to complete the course at their desired pace and on a schedule determined by them. Time Period Assignments Subject Matter Days 1-10 Module 1, Exam 1 Data and Statistics Days Module 2, Exam 2 Des. Statistics: Tabular / Graphical & Numerical Methods Days Module 3, Exam 3 Introduction to Probability Days Module 4, Exam 4 Probability Distributions Discrete and Continuous Days Module 5, Exam 5 Sampling and Sampling Distributions Days Module 6, Exam 6 Interval Estimation Days Module 7, Exam 7 Hypothesis Testing Days Module 8, Exam 8 Comparisons Involving Means Days Module 9, Exam 9 Regression Analysis Days Module 10, Exam 10 Various Tests Days Final Exam Comprehensive - including all course material Suggested External References: If the student desires to consult a reference for additional information, the following textbooks are recommended as providing complete treatment of the course subject matter. John S. Witte, Robert S. Witte, Statistics, Wylie 9 th Ed.

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