SD - Sampling Distribution Module Overview

Math_APStatBanner.png Sampling Distributions 

Introduction

In this unit have you will see how previously learned concepts and skills, like careful data collection and probability rules, culminate in a giant step forward in statistical understanding.   You will learn that the POWER of statistics lies in the ability to generalize over a broad population based solely on data gathered from one single sample.   Variation from sample to sample is not chaotic but rather displays a common pattern in the long run.   An important new theorem introduced in this unit, along with the Law of Large Numbers Theorem from earlier, will provide the foundation for further statistical exploration.

When generalizing to the population it is "daring" to use a single sample to form conclusions.   So we hypothesize about using many samples of the same size and look at them collectively to form our conclusions.    Not all distributions are symmetric and not all populations are normal...but the 68-95-99.7 rule is so powerful it would be nice to invoke it even in non-normal situations.   Therefore, normal calculations are still a large part of our calculations moving forward.

Essential Questions

  • Will every sample produce the same results?
  • How much variation can be expected?
  • What would the distribution of all possible samples look like?
  • How are normal calculations and sampling distributions associated?
  • Are there any theorems that can be applied to help us understand sampling distributions?
  • Why is the notion of sampling distributions so powerful?  

Key Terms

The following key terms will help you understand the content in this module.

Sampling Distributions Key Terms

Population parameter-  a numerically valued characteristic of a model for a population typically a measure of average, spread, or proportion

Sample statistic- values calculated for sampled data used to estimate the population parameter

Sampling variability- sampling is the act of drawing a portion to represent an entire population - repeated sampling produces variability in the resulting statistic

Sampling distribution- describes the expected behavior of a statistic when applied to repeated samples from the same population - each sample statistic is different and can be viewed as a random variable

Unbiased- a statistic used to estimate a parameter is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated

Central limit theorem- the sampling distribution of the mean approaches the normal distribution as the sample size increases regardless of the population distribution assuming independent observations

Law of large numbers- the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency as the number of trials increases

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