1. Sampling Distributions
Chapter 18

2. A sampling distribution is a model that describes how a sample proportion varies from sample to sample. Think of it as a collection of many different samples, each of which has a mean and standard deviation.
Parameters (p) describe the population, Statistics ( 𝑝 )describe a sample.
Categorical data is described by proportions. Quantitative data is described by means.
Central Limit Theorem: The mean of a random sample is a random variable whose distribution can be described by a Normal model. The larger the sample size, the better the approximation.
Essential Concepts

3. Sampling from Proportions
Proportions are based on success or fail options
𝜇 𝑝 =𝑝
SD( 𝑝 ) = 𝑝𝑞 𝑛
Assumptions
Independence
Sample Size
Conditions
Randomized sample
Less than 10% of total population
𝑛𝑝≥10, 𝑛𝑞≥10
Sampling from Proportions

4. Sampling from Means Quantitative data expressed as means. 𝑦 = 𝜇
SD( 𝑦 ) = 𝜎 𝑛
Assumptions
Independence
Sample Size
Conditions
Randomized sample
Less than 10% of total population
Sample is “Large Enough”; consider the context
Sampling from Means