We explore the varied uses of the uniform distribution on
as an example in the undergraduate probability and
statistics sequence or the mathematical statistics course.
Like its cousin, the uniform distribution on
this density provides tractable examples from the topic of
order statistics to hypothesis tests. Unlike its cousin,
which appears in many probability and statistics books,
this uniform is less well known or used. We discuss
maximum likelihood estimators, likelihood ratio tests,
confidence intervals, joint distributions of order
statistics, use of Mathematica®, sufficiency, and
other advanced topics. Finally, we suggest a few exercises
deriving likelihood ratio tests when the range is unknown
as well, or for the uniform on
Key Words: Confidence intervals; Efficiency; Estimation; Maximum likelihood; Sufficiency; Tests of hypotheses.
There has been much concern about making the curriculum for engineering statistics more relevant to the
needs of industry. One proposed solution is to include decision risk analysis in the curriculum. However,
the current coverage of decision risk analysis in statistics textbooks is either nonexistent or very
introductory. In part, this reflects the fact that decision risk analysis, as currently taught, relies on the
complex notion of a utility function.
Recent research in decision theory suggests a way of comprehensively and rigorously discussing decision
theory without using utility functions. In this new approach, the decision risk analysis course focuses on
making decisions so as to maximize the probability of meeting a target. This allows decision theory to be
integrated with reliability theory. This course would be more comprehensive than the conventional
introductory treatment of decision theory and no more difficult to teach. In addition, integrating
decision theory with reliability theory facilitates its incorporation in curricula that currently exclude
Key Words: Decision theory; Goal; Introductory statistics; Reliability theory; Utility function.
The purpose of the study was to develop a valid and reliable test instrument to identify students who
hold misconceptions about probability. A total of 263 students completed a multiple-choice test that
used a two-part format rather than the typical one-part format. Results of the study showed that even
students with formal instruction in statistics continue to demonstrate misconceptions. The test
instrument developed in this study provides instructors with (1) a valid and reliable method of
identifying students who hold common misconceptions about probability, and (2) diagnostic information
concerning students' errors not frequently available through other formats. The test instrument was
further evaluated in an instructional intervention study.
Key Words: Cognitive conflict; Group learning; Instructional intervention.
One of the main themes of statistics courses is to teach about variability, as well as location. This is
especially important for non-statistics students, who often overlook variability. We consider
particularly the problem of comparing variability among k samples (k > 2) that are not necessarily drawn
from Gaussian populations. This can also be viewed as testing for homoskedasticity of samples. We
examine tools for this problem from the perspective of their suitability for inclusion in elementary
statistics courses for students of non-mathematical subjects. The ideas are illustrated by an example
that arose in a student project.
Key Words: Homoskedasticity; Teaching statistics; Test; Variability.
Student-instructor and student-student interaction outside of the classroom are very important to
learning statistics. A successful statistics course Web site increases these interactions by creating a
forum for the instructor and students to communicate with statistical language. The development of a
successful statistics course Web site involves determining the Web site's purpose, deciding what Web
pages are needed, organizing the Web pages, implementing the Web site, and assessing the Web site. The
purpose of this article is to discuss the development of a statistics course Web site for a Web-enhanced
or Web-centric course and to provide a detailed example of one such course.
Key Words: Chat room; Internet; Message board; Web-centric; Web-enhanced; Web page.
Teaching Bits: A Resource for Teachers of Statistics
This department features information sampled from a variety of sources
that may be of interest to teachers of statistics. Deb Rumsey abstracts
information from the literature on teaching and learning statistics, while Bill
Peterson summarizes articles from the news and other media that may be used
with students to provoke discussions or serve as a basis for classroom activities
or student projects.
Many statistical problems can be satisfactorily resolved within the framework of linear regression.
Business students, for example, employ linear regression to uncover interesting insights in the fields of
Finance, Marketing, and Human Resources, among others. The purpose of this paper is to demonstrate
how several concepts arising in a typical discussion of multiple linear regression can be motivated
through the development of a pricing model for diamond stones. Specifically, we use data pertaining to
308 stones listed in an advertisement to construct a model, which educates us on the relative pricing of
caratage and the different grades of clarity and colour.
Key Words: Categorical variables; Data transformation; Multiple linear regression; Standardized