www.john-weber.com

Chapter 10: Sampling Distribution

Knowledge Prerequisites

Normal distribution

1. declarative knowledge (definitions)
   1. normal distribution
   2. 68-95-99.7 rule
2. procedural knowledge
   1. how to identify if a distribution is normally distributed
   2. how to identify mean and standard deviation of a normal distribution
   3. how to use the 68-95-99.7 rule to find the proportion (i.e., percentage) of area under a normal curve without a calculator
   4. how to find the proportion (i.e., percentage) of area under a normal curve using NDAREA program on TI-83
3. conditional knowledge
4. resources
   1. Chapter 3 of text

Sample

1. declarative knowledge (definitions)
   1. simple random sample (SRS)
2. procedural knowledge
   1. how to construct a SRS
3. conditional knowledge
4. resources
   1. Chapter 7 of text

Learning Goals

1. declarative knowledge (definitions)
   1. parameter
   2. statistic
   3. mean of population, $\mu$
   4. mean of sample, $\overline{x}$
   5. standard deviation of population, $\sigma$
   6. standard deviation of sample, $s$
   7. law of large numbers
   8. unbiased estimator
   9. central limit theorem (CLT)
2. procedural knowledge
   1. how to construct a sampling distribution
   2. how to calculate the mean of sampling distribution
   3. how to calculate the standard deviation of sampling distribution
   4. how to use the 68-95-99.7 rule to find the proportion (i.e., percentage) of area under a normal curve without a calculator
   5. how to find the proportion (i.e., percentage) of area under a normal curve using NDAREA program on TI-83
3. conditional knowledge
   1. know difference between parameter and statistic
   2. know why the sampling distribution is important
   3. recognize similarities and differences between distribution of population and sampling distribution
   4. know shape of sampling distribution
   5. know the difference between the Law of Large Numbers and the Central Limit Theorem (CLT)

Questions to Ponder

1. What is the best way to study/prepare for the concepts in this section? Are there are other methods to study these concepts?
2. What questions do you need to ask the instructor?

Purpose of this Section

Read p. 249 of your text. A sampling distribution describes the behavior of a sample statistic (e.g., the sample mean) by noting what happens to the statistic for many different samples of the same size. Also, the Central Limit Theorem is essential for hypothesis testing.

General Notes

You are NOT responsible for statistical control, $\overline{x}$ charts or process control.

Activity

M&Ms

Resources

• Sampling Distributions [and Central Limit Theorem] - http://academic.udayton.edu/gregelvers/psy216/rvls/stat_sim/sampling_dist/ - This java applet lets you explore various aspects of sampling distributions.
• Central Limit Theorem - http://www.stat.vt.edu/~sundar/java/applets/CLT2Applet.html - This applet demonstrates the central limit theorem for a variety of distributions.

Back to John Weber's MATH 1431 Page

Back to john-weber.com