Ch. 7 Important Information Sheet
Chapter 7: Sampling Distributions
Unit 5: Sampling Distributions
Important Information and Definitions
A statistic is a number that describes some characteristic of a sample.
A parameter is a number that describes some characteristic of a population.
| Sample statistic | Population Parameter | |
|---|---|---|
| (the sample mean) | estimates | μ (the population mean) |
| (the sample proportion) | estimates | p (the population proportion) |
| (the sample st. dev.) | estimates | σ (the population st. dev.) |
Sampling variability refers to the fact that different random samples of the same size from the same population produce different values for a statistic.
The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.
A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the value of the parameter being estimated.
The variability of a statistic is described by the spread of its sampling distribution. Larger samples result in sampling distributions with less variability.
The sampling distribution of the sample proportion , describes the distribution of values taken by the sample proportion in all possible samples of the same size from the same population.
The mean of the sampling distribution of is 
The standard deviation of the sampling distribution of is 
as long as the 10% condition is satisfied.
The sampling distribution of p-hat is approximately Normal as long as the Large Counts condition is satisfied.
The sampling distribution of 
The mean of this sampling distribution is 
The standard deviation of this sampling distribution is: 
as long as the 10% condition is met for both samples.
The shape of this sampling distribution is approximately Normal if the Large Counts Condition is met for both samples.
The sampling distribution of the sample mean describes the distribution of values taken by the sample mean in all possible samples of the same size from the same population.
The mean of the sampling distribution of is 
The standard deviation of the sampling distribution of is 
as long as the 10% condition is met.
Draw an SRS of size n from any population with mean and standard deviation . The central limit theorem (CLT) says that when n is sufficiently large, the sampling distribution of the sample mean is approximately Normal. *what is large though? When n is greater than or equal to 30.
The sampling distribution of 
The mean of this sampling distribution is 
The standard deviation of this sampling distribution is 
as long as the 10% condition has been met.
The shape of this sampling distribution is Normal if both populations are Normal. It is approximately Normal if the Central Limit Theorem has been satisfied for both samples.
WARNING: Notation matters! The symbols 
all have specific and different meanings. Either use notation correctly, or don’t use it at all. You can expect to lose credit if you use incorrect notation.