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Johnson County Community College
Statistics (Math 181)
7.1 Paired Designs
In Chapter 6, we had problems with two means, but these means came from "Independent Groups" which
were being compared.
In Chapter 7, we'll learn how to perform a hypothesis test or construct a confidence interval in order to
compare two means from paired sets of data. (Paired Design)
The first question that must be asked when comparing two means from two samples is whether the two
populations are two independent samples (Chapter 6) or are, in fact, one sample of related pairs (Chapter
Here are some scenarios to help us determine the difference:
1. A school cafeteria offers a vegetarian and non-vegetarian option for lunch every day. For a period of two
weeks, you record how many calories are in the vegetarian option and how many calories are in the non-
vegetarian option. Your goal is to see if the vegetarian options tend to differ with regard to the average
number of calories from nonvegetarian options.
Paired Data - 2 Pieces of information for each day
2. Does higher-octane level in gasoline improve gas mileage?
( vey + non - veg ).
To answer this question, a researcher randomly selected 15 individuals (and their cars) to participate in a
study. Each participant received 10 gallons of gas (twice, once with 87-octane gas and once with 92-
octane gas) and drove his or her car on a closed course that simulated both city and highway driving.
The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine
whether the car filled up with 87-octane or 92-octane gas first, and the driver did not know which type
of fuel was in the tank.
Paired dater -. each car had two mileages recorded .
3. You wonder whether students on your campus tend to drive newer cars than faculty. You take a random
sample of 20 students and a random sample of 10 faculty members and ask each person how old their
4. During the first weekend of August each year, Twinsburg, Ohio celebrates its annual "Twins Day in
Twinsburg" festival. Scientists visit the festival because of the opportunity to study identical twins. A
study of twins showed that myopia (near-sightedness) is strongly affected by hereditary factors, not
environmental factors such as watching television or playing computer games.
Paired data - each set of twins is a set of dates,
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- Spring '17