## Instructors' Notes

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 Applet 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 applet.

In 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

#### 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 Exercise questions.

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 WISE p-z converter. Java and JavaScript must be enabled on students’ browsers to use many features of the SDM tutorial. Most students complete Exercise 1 in less than 45 minutes.

#### 3. Review

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 answered interactively 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 printed-out exercise to be submitted and evaluated.