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Faculty of Science Mathematics & Statistics
Faculty of Science

# STATS 2MB3, Winter 2019

STATISTICAL METHODS AND APPLICATIONS

"Statistics is the science, the art, the philosophy, and the technique of making inferences from the particular to the general", is a well-known quote attributed to John W. Tukey, one of the greatest statisticians of all times. With a strong footing on applications, this course demonstrates the statement repeatedly all along its flow. The course objectives}are to learn, exemplify and train the student on: (a) methods to summarize data numerically and graphically, (b) the most widely used statistical methods to draw inferences from observed data, (c) some of the mathematical details behind the methods, and (d) handling data and carrying out basic statistical analyses using the statistical package R. The course begins with a variety of graphical and numerical methods to summarize data. Among them are the stem-and-leaf and dot plots, the histogram and the boxplots, as well as the mean, trimmed mean, median, variance and standard deviation for datasets. Each of these methods is illustrated with real datasets from engineering, science and other areas. The next stop is at the manipulation of linear combinations of random variables} and their properties such as means and variances. Many of the statistics used for estimation and inferences about parameters are linear combinations of the sample values. A giant of statistics is the Central Limit Theorem regarding the distribution of the sample mean, a good number of illustrations are discussed in detail. This is in preparation for tackling methods to derive estimators for population parameters such as a population mean or a population proportion. The two main methods taken up are the Method of Moments and the Method of Maximum Likelihood. After that we focus on inferences for population parameters such as confidence intervals and tests of hypotheses. The appropriate methods to be used depend on what is known about the target population. The three main methods studied are the z method based on the normal distribution, the t method based on the Student's t distribution, and the chi-squared method. There will be a few Lab sessions dedicated to training in R. The prerequisite course STATS 2D03 provides quite sufficiently all the background material needed for the course.

INSTRUCTOR:  A. Canty

Course Website

Calendar Description
3 Units
Estimation; sampling distributions; confidence intervals; hypothesis testing, power; linear regression; graphical and computational methods.
Three lectures, one tutorial; one term
Prerequisite(s): STATS 2D03
Not open to students with credit or registration in ARTSSCI 2R03 or PNB 3XE3.

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Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
L8S 4K1

### Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West