Chess Tournament: Review the Rating Evidence

Decide when a sample can support a claim about a larger group.

Check the Records

A chess club tournament has 96 entrants. A rating is a numerical estimate of a player's chess strength. Evaluate the records used in each investigation.

The organizer has the current rating of every tournament entrant and wants to describe those entrants' ratings. Which statement is correct?

A. The organizer has data for the whole population of interest.B. The organizer can use these records to describe all chess players.C. The organizer has a random sample because ratings are numbers.D. The organizer must select a sample before describing the entrants.

The tournament archive contains 288 game records. Priya randomly selects 32 different records from the complete archive and checks the number of moves in each game. What can this sample most directly help describe?

A. The number of moves in all games played at other clubs.B. The number of moves in games played at this tournament.C. The current ratings of everyone who plays chess in town.D. The current ratings of players entered in this tournament.

Omar wants to sample all 96 tournament entrants, but his selection list contains only the 72 entrants who registered early. Everyone else registered later.

How many entrants have no chance of selection from this list? entrants

Omar wants his rating sample to represent all tournament entrants. Which change best fixes the problem with using only the early-registration list?

A. Update the list to include everyone before selecting randomly.B. Select more names at random from the early-registration list.C. Use only the early registrants with the most recent ratings.D. Ask the early registrants to suggest players for the sample.

Inspect the Selection

For these investigations, the population is all 96 tournament entrants. Consider how each selection rule could affect the sample.

Each entrant has a different ID from 1 through 96. Which computer procedure selects a random sample of 16 different entrants?

A. Select the 16 IDs belonging to the highest-rated entrants.B. Draw 16 different IDs randomly from all 96 possible IDs.C. Select IDs 1 through 16 because they are easy to locate.D. Draw 16 different IDs randomly from IDs 1 through 48.

A computer selects 16 different entrants at random from the complete roster, giving every entrant the same chance. The organizer keeps all 16 selected entrants in the sample. Select every true statement.

A computer randomly selects 20 entrants from the full roster. Before reviewing their ratings, an organizer removes every selected entrant who lost in round one. Which judgment is best?

A. The remaining group represents everyone because losses are recorded.B. The remaining group improves the sample because fewer records remain.C. The remaining group may favor stronger players because losses affect inclusion.D. The remaining group is still random because the first step was random.

Lena uses the club's online profile directory to select a rating sample. The directory is missing some entrants, as shown below.

Tournament Entrants and Online Profiles
Rating group	All entrants	Have online profiles
Below 1000	40	12
1000 or above	56	56

Why is a random sample from this directory a poor choice for describing all entrants' ratings?

A. Many lower-rated entrants cannot be selected from the directory.B. Every higher-rated entrant will automatically enter the sample.C. A directory cannot be used for any kind of random selection.D. The two rating groups must have equal numbers of entrants.

A reporter wants to learn how satisfied all entrants were with their opponents' rating levels. The reporter selects entrants randomly only from those who won prizes. Why does random selection within this group not solve the main problem?

A. Prize winners cannot answer questions about their opponents.B. Random selection requires using game records instead of people.C. A sample must include every entrant to provide useful evidence.D. Entrants who won no prize have no chance of being represented.

Judge the Claims

Decide what the evidence supports. A useful sample gives information about a population without guaranteeing an exact match.

10.

Eighteen entrants are randomly selected from the complete roster. All respond, and most say their rating helped them set a realistic tournament goal. Which report is best supported?

A. The results prove that every entrant used a rating to set a goal.B. The results prove that entrants with higher ratings set better goals.C. The results suggest that many tournament entrants found ratings useful.D. The results establish how every chess club member sets tournament goals.

11.

The organizer wants to sample entrants to learn whether they support rating-based awards. Select every plan that gives each entrant an equal chance of being selected.

12.

A tournament newsletter says, “Random samples tend to represent the population well.” Which explanation best describes why?

A. Chance selection makes the smallest sample identical to the population.B. Chance selection ensures that every rating appears equally often.C. Chance selection prevents any unusual group from entering the sample.D. Chance selection avoids systematically favoring entrants with particular traits.

13.

To select entrants for a rating review, Mateo puts three identical slips into a container for each entrant rated 1000 or above and one identical slip for each entrant rated below 1000. He mixes the slips thoroughly and draws one. Mateo says, “Every entrant has a chance, and I cannot see the names, so this is a fair way to represent all entrants.” Explain what is wrong with his reasoning and how to improve the method.