TRI-COUNTY TECHNICAL COLLEGE
COURSE SYLLABUS
Course Prefix & Number: _MAT 220______________
Course Title: _Advanced Statistics______
Class Hours Lab Hours Credits
Per week: _3_ Per Week: _0_ Awarded: _3_
Catalog Description: This course includes the following topics: estimation of parameters; formulation and testing of hypotheses; multiple and non-linear regression; correlation; contingency tables; analysis of variance; special distributions; introduction to nonparametric statistics.
Entry Level Skills: Interpret graphs; calculate measures of central tendency, dispersion, and position; determine correlation; regression analysis; know probability rules; use probability distributions; construct hypothesis tests and confidence intervals.
Pre-requisites: MAT 120 with a grade of C or better.
Co-requisites: none
Text(s)/Required Materials: Elementary Statistics by Mario F. Triola, 10th edition, Addision-Wesley, 2003.
Course Competencies and Objectives/ Major Topics:
Unit 1: Estimates and Hypothesis Testing for a Single Population
Upon completion of this unit (7-1 – 7-5 and 8-1 – 8-6) the student should be able to:
1. Identify the best point estimate for m and p;
2. Construct confidence intervals for m (large and small samples) and p;
3. Determine the sample sizes necessary to estimate parameters to within given tolerance factors;
4. Determine the components of a hypothesis test: null hypothesis, alternative hypothesis, type I error, type II error, test statistic, significance level, critical region, critical value, decision, and statement of conclusion;
5. Apply both the traditional method and P-value method to test hypotheses about means (large and small samples), proportions, and standard deviations or variances.
Unit 2: Inferences About Two Populations
Upon completion of this unit (9-1, 9-3, 9-4, and 13-1 – 13-3) the student should be able to:
1. Test hypotheses about the means of two populations using independent and large samples, and construct confidence intervals to estimate the difference between two population means;
2. Test hypotheses about the means of two populations using dependent samples (consisting of paired data), and construct confidence intervals as estimates of the difference between two population means;
3. Apply the sign test to test the claim that two sets of dependent data have the same median;
4. Apply the Wilcoxon signed-rank test to test the claim that two sets of dependent data come from identical populations;
5. Use Minitab or Statdisk statistical software to construct confidence intervals and perform hypothesis tests for cases involving two populations.
Unit 3: More Inferences About Two Populations
Upon completion of this unit (9-2, 9-5 and 13-4) the student should be able to:
1. Test claims about the difference between two population proportions and construct confidence intervals for estimating the difference between two population proportions;
2. Test hypotheses made about two population variances or standard deviations;
3. Apply the Wilcoxon rank-sum test to test the claim that two independent samples come from identical populations;
Unit 4: Correlation & Regression
Upon completion of this unit (10-1 – 10-6 and 13-6) the student should be able to:
1. Use the scatter diagram and a hypothesis test about the linear correlation coefficient r to decide whether there is a linear relationship between two variables;
2. Find the equation of the regression line which, by the least squares criterion, best fits the paired data;
3. Use the regression equation to calculate a point estimate of the predicted value of one variable, given some particular value for the other variable;
4. Interpret the coefficient of determination r2 as the amount of the total variation in y that can be explained by the regression line;
5. Construct a prediction interval estimate for an individual value of y;
6. Use Minitab statistical software to produce a multiple regression equation, the adjusted coefficient of determination R2, and a P-value to measure the overall significance of the multiple regression equation, and interpret these results;
7. Identify the mathematical model that best fits given data, considering linear, quadratic, logarithmic, exponential, and power models;
8. Use the rank correlation coefficient to test for an association between two sets of paired data.
Unit 5: Multinomial Experiments & Contingency Tables; ANOVA
Upon completion of this unit (11-1 – 11-3, 12-1 – 12-2 and 13-5) the student should be able to:
1. For multinomial experiments, use the goodness-or-fit procedure of hypothesis testing to test claims that observed sample frequencies fit a particular distribution;
2. For contingency tables, perform the test of independence between the row and column variables, as well as the test of homogeneity;
3. Use the method of one-way analysis of variance (ANOVA) to test hypotheses that three or more population means are equal, including interpretation of Minitab results;
4. Apply the Kruskal-Wallis test to test the claim that several independent samples come from identical populations.
GUIDELINES FOR GROUP PROJECT
The group project will give students an opportunity to apply methods of statistics to real data. Students may conduct experiments to collect raw data or may research data already obtained. Chapter 15 contains suggested topics and help with determining which specific procedure is most appropriate.
Students should follow these guidelines for their group projects. Each group should have 2-4 members, and each member of the group should do an equal share of work. The data set to be analyzed must be approved by the instructor. A rough draft of progress should be submitted to the instructor about the end of the tenth week of the semester. The formal written report should be submitted at least two days before the oral presentation.
Oral reports (5- to 10-minutes) will be given during the last week of the semester.
The typewritten report must include the following components:
1. List of data collected.
2. Description of the method of analysis.
3. Relevant graphs and/or statistics, including Minitab displays.
4. Statement of conclusions.
5. Reasons why the results might not be correct, along with a description of ways in which the study could be improved, given more time and money.
Grade Calculation Method: Unit Tests = 60 – 70%
Group Project = 15 – 20%
Homework/other = 0 – 10%
Final Exam = 15 – 20%_
100%
Additional Information Pertaining to Grades: a grade of C or better is required for university transfer credit
Prepared by:_Debra Bindschatel__ Date written or revised:_03/03/2006______