Question

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 the more than $20,000$ fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over $\backslash (100$ each, while seats in the top rows of the arena cost $\backslash )25$ each. The arena is divided into $30$ numbered sections, from $101$ to $130$ Each section has rows of seats labeled with letters from A (nearest the court) to $ZZ$ (top row of the arena).

$3$ Which would be a better way to take a cluster sample of fans: using the lettered rows or the numbered sections as clusters? Explain.

Short answer

The arena has been divided in to numbers from $101$ to $130$

Step-by-step solution

Given information

Ticket prices for the game range from over $\$100$ for tickets close to the court to $\$25$ for seats in the top rows of the arena. The arena is divided into $30$ sections, numbered 101 through $130$

Concept

Divide the population into smaller groups before taking a cluster sample. These groups should ideally reflect the population's features. Then pick one of the clusters' SRS. The sample includes all individuals in the designated clusters.

Explanation

The best approach is to build strata with people who have similar characteristics. The ideal approach would be to choose the lettered row as the strata because the distance between the lettered and the ticket price is the same. As a result, the optimal method is to choose letters with the same distance and price.