How the Sampling Distribution of the Mean tutorial fits into the typical
statistics course: WISE tutorials are stand-alone modules that are
independent from other tutorials but designed to complement each other when
used in conjunction. This affords the instructor maximum flexibility in using
WISE tutorials in a curriculum tailored to specific learning goals.
The Sampling Distribution of the Mean (SDM) Tutorial assumes that
students have some familiarity with basic elementary statistics, such as
means, standard deviation, variance, and the normal distribution, and
sampling distributions. The SDM tutorial includes optional links to brief
reviews of z-scores and normal distributions as well as the Central
Limit Theorem (CLT). Following the SDM tutorial, students may complete the
CLT Theorem Module, which is intended to prepare students to learn
about hypothesis testing and confidence intervals.
When to use the SDM tutorial? The SDM Exercise 1 demonstrates how
sample size affects the shape of the sampling distribution of the mean.
Instructors may use the SDM module after introducing basic descriptive
statistics, such as the mean and standard deviation, and before discussing
parametric statistics and hypothesis testing. The tutorial offers
students the chance to apply the standard normal distribution in calculating
the probability of obtaining certain values.
Suggestions for Using the SDM Tutorial
- Class demonstration/Lecture Aid
- Lab assignment
- Homework assignment
- Review assignment
The SDM tutorial and its components may be incorporated into your
classroom curriculum in several ways. Here are some suggestions:
1. Live Demonstration
As part of either a lecture or guided lab assignment, the SDM
itself may be used by the instructor to visually demonstrate different
aspects of the sampling distribution. Some instructors may choose to
step through parts or all of the tutorial in a demonstration mode.
This demonstration may serve as a stimulus for classroom discussion
and/or introduction to an assignment for students. See our
step-by-step guide for a live demonstration using the
particular, instructors may use the applet to demonstrate
the relevance of the CLT to distributions of any shape. The
applet provides options for normal, binomial, and uniform
distributions. Samples drawn from all of
these distributions, given that samples are large enough,
produce normal sampling distributions
Demonstration Guide | Instructions for Using
2. Post-lecture Assignment
The major portion of the tutorial, Exercise 1, may be used as either a
guided lab exercise or an independently-completed homework assignment to
reinforce and explore statistical concepts introduced by the instructor
during lecture. Although answers
to selected Exercise questions are provided, students still need to draw their
own conclusions throughout the Exercise and integrate information in response to
Before completing Exercise 1, students may print the Exercise pages either in
their entirety [the
Tutorial pages] or an answer only sheet
[the Worksheet pages]
to write down their responses and calculations as they work through the Exercise.
Alternatively, students may complete the Exercise online and then print out either set
of these pages which will automatically include their online responses. Instructors
may ask students to submit additional pages showing their calculations.
For z-probability calculations, students may use either a table
for the standardized normal distribution (z) or the
enabled on students’ browsers to use many features of
the SDM tutorial. Most students complete Exercise 1 in less than 45 minutes.
For more information, see the introduction
to the tutorial.
Exercise 1 involves p-z calculations integrated with drawing
samples of different sizes using the SDM applet. Supplemental reviews
briefly cover z-scores and the Central Limit Theorem.
Additional review of major concepts concerning the sampling
distribution of the mean is supported by two sections in the
tutorial: review questions and follow-up questions. These questions
may be assigned independently of the Exercise questions.
The review questions are seven multiple choice questions that may be
online or on a printed-out
version that students may turn in to the instructor. Students have access to
the answers to the review questions in the interactive version.
The follow-up questions require open-ended responses and are more conceptual
than the review questions. As answers to follow-up questions are not posted
online, these questions may be downloaded as a
to be submitted and evaluated.
We hope this tutorial is helpful for you and your students, and we
welcome your feedback on this tutorial and other aspects of the WISE site.
Please send your comments to firstname.lastname@example.org.
Questions, comments, difficulties? See our
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