Chapter 8: Sampling Variability and Sampling Distributions
Key Terms and Concepts
| Statistic | Any quantity whose value is computed from sample data. |
| Sampling Distribution | The probability distribution of a statistic: The sampling distribution describes the long-run behavior of the statistic. |
Sampling Distribution of  |
The probability distribution of the sample mean
, based on a random sample of size n.
Properties of the
sampling distribution: 
and 
(where 
and 
are the population mean and standard
deviation, respectively). In addition, when the population distribution is normal or the
sample size is large, the sampling distribution of
is (approximately) normal. |
| Central Limit Theorem | This important theorem states that when n is sufficiently
large, the
distribution will be approximately
normal. The standard rule of thumb is that the theorem can safely be applied when n
exceeds 30. |
| Sampling distribution of p | The probability distribution of the sample proportion p,
based on a random sample of size n. When the sample size is sufficiently large,
the sampling distribution of p is approximately normal, with 
and 
(where 
is the true population proportion). |
Notes from Mrs. Caso
|
All of the formulas and important information can be found in the "Key Terms & Concepts" table above and: |
|
|
The farther the value of π is from 0.5, the larger n must be in order for the normal approximation to the sampling distribution of p to be accurate. A conservative rule of thumb is that both nπ ≥ 10 and n( 1 - π) ≥ 10, then it is safe to use the normal approximation. |
|
Also, review the following: Figure 8.5 |
Interactive Materials
-
Central Limit Theorem is a Java Applet to illustrate this important theorem....
Check it out.
Schedule
| Timeline: | 9 days | |
| Day 90: 01/21/14 |
Discussion: Section 8.1 | Against All Odds: Unit 22 |
| Day 91: 01/22/14 |
Discussion: Exercises 8.1, 8.2, 8.3, 8.6, & 8.9 | MINITAB Lab: 8-1 |
| Day 92: 01/23/14 |
MINITAB Lab: 8-1 (finish) | Discussion: Section 8.2 |
| Day 93: 01/24/14 |
Discussion: Exercises 8.10, 8.11, 8.13, 8.16, 8.19, & 8.22 | Activity: Cents and the Central Limit Theorem. |
| Day 94: 01/27/14 |
Activity: Cents and the Central Limit Theorem. (finish) | MINITAB Lab: 8-2 |
| Day 95: 01/28/14 |
MINITAB Lab: 8-2 (finish) | Discussion: Section 8.3 |
| Day 96: 01/29/143 |
Discussion: Exercises 8.23, 8.24, 8.25, 8.28, & 8.31 | |
| Day 97: 01/30/14 |
Review: Supplementary Problems 8.32 - 8.37 (all) | |
| Day 98: 01/31/14 |
Take Test: Chapter 8 | |