Sampling Distributions Chapter 18

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

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

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