Stat 226 - Section 8.1

# Stat 226 - Section 8.1 - Introduction Chapter 8 Inference...

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Chapter 8 Inference for Proportions Chapter 8 1 Introduction Chapter 7 addressed inference for the population mean μ . These ideas apply only to quantitative variables such as price, height, time, etc. In some studies, we may have categorical variables about which we would like to make inference. Some examples are gender, occupation, voting choice, etc. Counts or proportions are statistics that describe categorical variables in a sample. Chapter 8 2 Proportions When we make inference for a categorical variable, usually the parameter of interest is a population proportion . A population proportion p is a fraction or percentage of the population that falls into a particular category. By definition, these proportions would have values somewhere between 0 and 1. Like for the population mean, the sampling distribution for a proportion is approximately Normal for large sample sizes. Chapter 8 3 Section 8.1 Inference for a Single Proportion Section 8.1 4 Example - Vehicle Ownership A market researcher is interested in attitudes and behavior related to new vehicle purchases in the Midwest. The researcher identifies several variables of interest, including gender, age, marital status, type of vehicle purchased, vehicle size, and the manufacturer or “make” of the vehicle. Most of the variables here are categorical. The researcher is interested in making confidence intervals for several population parameters. Section 8.1 5 Manufacturing Location The researcher surveys a random sample of 303 adults from across the Midwest. One variable of interest is the manufacturer for vehicles purchased. The researcher classified manufacturers into three categories based on company origin.

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