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Chapter 4: Q. 4.3 (page 287)

The manager of a sports arena wants to learn more about the financial status of the people who are attending an NBA basketball game. He would like to give a survey to a representative sample of about10%of the fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over \(200each, while seats in the top rows of the arena cost \)50each. The arena is divided into 50numbered sections, from 101to150. Each section has rows of seats labeled with letters from A(nearest the court) toZZ (top row of the arena).

a. Explain why it might be difficult to give the survey to an SRSof fans.

b. Explain why it would be better to select a stratified random sample using the lettered rows rather than the numbered sections as strata. What is the benefit of using a stratified sample in this context?

c. Explain how to select a cluster sample of fans. What is the benefit of using a cluster sample in this context?

Short Answer

Expert verified

a. We would need to randomly select10%the seats and then find every person who was seated in that seat, which will be very time-consuming.

b. We are able to take into account the effect that the cost of the ticket has on the opinion.

c. The answers could vary. For example All individuals in 5randomly selected number sections.

Step by step solution

01

Part (a) step 1: Given Information

We need to explain whether it might be difficult to give the survey to an SRSof fans.

02

Part (a) step 2: Explanation

Simple random sampling uses a sample of size nin which every sample of size nhas an equal chance of being chosen.

It is not practical to get a simple random sample (SRS)from the fans, because we would need to randomly select 10%of the seats and then find every person who was seated in that seat, which will be very time-consuming.

Moreover, we would then still need to take the survey from each of these people, once the people were found.

03

Part (b) step 1: Given Information

We need to explain whether it would be better to select a stratified random sample using the lettered rows rather than the numbered sections as strata.

04

Part (b) step 2: Explanation

Stratified random sampling draws simple random samples from independent subgroups (stratum).

we using the lettered rows as strata will be better than using the numbered sections as strata because the numbered sections are all similar when the lettered rows as not similar, so the seats near the court cost the most, while the seats in the top row cost the least.

If we would then use the lettered rows as strata, then this would allow us to compare the opinion of the fans to the cost of their ticket and thus we are able to take into account the effect the cost of the ticket has on the opinion.

05

Part (c) step 1: Given Information

We need to explain how to select a cluster sample of fans. What is the benefit of using a cluster sample in this context.

06

Part (c) step 2: Explanation

Cluster sampling divides the population into non-overlapping subgroups and some of these subgroups are then in the samples.

The 50numbered sections are nonoverlapping subgroups, which are also similar.

If we randomly select 5to50numbered sections, then we have randomly selected 10%of the numbered sections and thus we selected 10%of the fans.

A possible cluster sample then contains all individuals in 5randomly selected number sections.

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