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Chapter 4: Q 21. (page 228)

Go Blue! Michigan Stadium, also known as 鈥淭he Big House,鈥� seats over 100,000 fans for a football game. The University of Michigan athletic department plans to conduct a survey about concessions that are sold during games. Tickets are most expensive for seats near the field and on the sideline. The cheapest seats are high up in the end zones (where one of the authors sat as a student). A map of the stadium is shown.100,000

(a) The athletic department is considering a stratified random sample. What would you recommend as the strata? Why?

(b) Explain why a cluster sample might be easier to obtain. What would you recommend for the clusters? Why?

Short Answer

Expert verified

Part (a) Sideline, Corner and End zone.

Part (b) The single people in the simple random samples as they are spread over randomly overall boxes.

Step by step solution

01

Part (a) Step 1: Given information

No. of fan seats for a football game, n=100,000

Also, tickets on the sidelines are the most expensive, while the cheapest seats are in the end zones.

02

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Part (a) Step 3: Explanation

The University of Michigan sports department intends to undertake a poll about game-day concessions. Seats near the pitch and on the sidelines are the most expensive. Simple random samples are obtained from independent subgroups using stratified random sampling. The strata are separate subgroups. The price of deception is the same for all three sections: sideline, corner, and the end zone. Furthermore, each person will be assigned to a specific section. As a result, the following strata should be used: sideline, corner, and the end zone.

04

Part (b) Step 1: Explanation

Simple random samples are obtained from independent subgroups using stratified random sampling. Cluster sampling separates the population into non-overlapping subgroups, which are subsequently included in the sample. All of the sitting boxes (1-44) are divided into subgroups, with some subgroups being chosen. It will be easy to pick individuals because all persons from a few boxes will be included in the sample, allowing us to simply place people at the entrances of those boxes to conduct surveys of the people who live there. Part (a) will be much more challenging because we will need to draw a simple random sample from the sideline/corner/end zone strata, and it will be much more difficult to discover and interview people.

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Most popular questions from this chapter

In an interesting experiment, researchers examined the effect of ultrasound on birth weight. Pregnant women participating in the study were randomly assigned to one of two groups. The first group of women received an ultrasound; the second group did not. When the subjects鈥� babies were born, their birth weights were recorded. The women who received the ultrasounds had heavier babies.

Did the experimental design take the placebo effect into account? Why is this important?

Baseball tickets Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season. You get permission from the team鈥檚 management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club seating or box seats (the most expensive seating). Using a computer,

you randomly select 500 seats from the rest of the stadium. During the game, you ask the fans in those seats how much they spent that day.

(a) Provide a reason why this survey might yield a biased result.

(b) Explain whether the reason you provided in (a) is a sampling error or a non sampling error.

Two essential features of all statistically designed experiments are

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(e) use enough subjects; always have a control group.

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