SPA 3e_ Teachers Edition _ Ch 6

Promoting Good Habits and Skills
Chapter 6 is about the characteristics of sampling distributions.
The sampling distribution of the sample proportion
and sample mean will play a key role in Chapters 7–9, so
understanding them is very important for future success.
Here are some important habits to develop in your students
as you teach Chapter 6:
1. Pay attention to the vocabulary: Understanding the differences
among population, parameter, sample, and statistic is
absolutely vital to understanding this and future chapters.
Also, make sure your students understand the difference
between the distribution of the population, the distribution
of a single sample, and the sampling distribution. They are
not the same!
2. Emphasize symbols, not formulas: The symbols used in
this chapter are quite standard in all of statistics. While we
don’t want the symbols to overwhelm students, they are
an integral part of basic statistical practice. The symbols
n, p, p^ , m, s, and x will be used extensively in Chapters
7–9. Being comfortable with them now will be of great
help later. On the other hand, don’t have students memorize
the formulas for the mean and standard deviations of
the sampling distributions in this chapter. Having students
understand the symbols is far more important than having
them memorize the formulas.
3. Look for the underlying variable: If your students can
recognize the underlying variable and classify it as categorical
or quantitative, they can tell which sampling distribution
is appropriate. Categorical variables (like color of
a Reese’s Pieces ® candy) lead to sample counts and sample
proportions. Quantitative variables (like the year a penny
was manufactured) lead to sample means. Developing this
skill now will pay dividends in future chapters as well!
4. Think back to the simulations: Because sampling distributions
are very abstract, simulating the sampling process can
provide insight for students. If students have trouble understanding
the different distributions in sampling situations,
have them think back to concrete simulations like the
“A penny for your thoughts?” activity in Lesson 6.1 and
computer simulations with software like the SPA applets.
Physical simulations are so important for student understanding
that if you were to do only one activity in the entire
chapter, it should be the penny activity.
5. Watch the conditions: Students will often pay little attention
to the conditions about sampling distributions. Have
them focus on the Large Counts condition and the Normal/
Large Sample condition because these concepts will be used
repeatedly in future chapters. If students don’t pay attention
to them now, they will have a more difficult time in the
future.
Lesson-by-Lesson Content
Overview
Lesson 6.1 What Is a Sampling Distribution?
A large collection of individuals is called a population.
A subset of that population is called a sample. A number
that measures some characteristic of a population is
called a parameter, while a numerical measure of some
characteristic of a sample is called a statistic. Statistics
vary from sample to sample. The distribution of values
taken on by a statistic from every possible sample of a
given size is called the sampling distribution of that statistic.
We can evaluate claims about a parameter by calculating
probabilities from the sampling distribution of
the corresponding statistic.
6-4
C H A P T E R 6 • Sampling Distributions
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