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Dalton conducted a survey of randomly selected students with Education Galaxy accounts to determine students' favorite games. The table shows the results of the survey.

Favorite Education Galaxy Games

Game Number of Students
Blast Off 47
Boss Battles 60
Galaxy Defenders 52
Rocket Ship 40
Space Cracken 29
Stardust 34
Wormhole 38

Which inferences about all students with Education Galaxy accounts appear to be valid?

(choose 2)
Responses
A The number of students who like Wormhole or Blast Off best is less than the number of students who like Rocket Ship or Stardust best.The number of students who like Wormhole or Blast Off best is less than the number of students who like Rocket Ship or Stardust best.
B One out of every five students considers Boss Battles their favorite Education Galaxy game.One out of every five students considers Boss Battles their favorite Education Galaxy game.
C The number of students who like Blast Off best is greater than the number of students who like Wormhole, Space Cracken, or Stardust best.The number of students who like Blast Off best is greater than the number of students who like Wormhole, Space Cracken, or Stardust best.
D The number of students who like Galaxy Defenders best is less than the number of students who like Rocket Ship or Space Cracken best.The number of students who like Galaxy Defenders best is less than the number of students who like Rocket Ship or Space Cracken best.
E The number of students who like Boss Battles best is greater than the number of students who like Rocket Ship or Galaxy Defenders best.

1 answer

To evaluate the validity of the inferences based on the survey results, let's analyze each option using the provided game preference data:

  1. Blast Off: 47
  2. Boss Battles: 60
  3. Galaxy Defenders: 52
  4. Rocket Ship: 40
  5. Space Cracken: 29
  6. Stardust: 34
  7. Wormhole: 38

Now let's analyze the options:

A. The number of students who like Wormhole or Blast Off best is less than the number of students who like Rocket Ship or Stardust best.

  • Wormhole (38) + Blast Off (47) = 85
  • Rocket Ship (40) + Stardust (34) = 74
  • This statement is false because 85 is greater than 74.

B. One out of every five students considers Boss Battles their favorite Education Galaxy game.

  • Total number of students surveyed = 47 + 60 + 52 + 40 + 29 + 34 + 38 = 300 students
  • One out of every five students equates to 300 / 5 = 60 students.
  • This statement is true since 60 students like Boss Battles.

C. The number of students who like Blast Off best is greater than the number of students who like Wormhole, Space Cracken, or Stardust best.

  • Blast Off (47) > (Wormhole (38) + Space Cracken (29) + Stardust (34)) = 101.
  • This statement is false because 47 is not greater than 101.

D. The number of students who like Galaxy Defenders best is less than the number of students who like Rocket Ship or Space Cracken best.

  • Galaxy Defenders (52) < (Rocket Ship (40) + Space Cracken (29)) = 69.
  • This statement is true because 52 is less than 69.

E. The number of students who like Boss Battles best is greater than the number of students who like Rocket Ship or Galaxy Defenders best.

  • Boss Battles (60) > (Rocket Ship (40) + Galaxy Defenders (52)) = 92.
  • This statement is false because 60 is not greater than 92.

From the analysis, the valid inferences are:

  • B. One out of every five students considers Boss Battles their favorite Education Galaxy game.
  • D. The number of students who like Galaxy Defenders best is less than the number of students who like Rocket Ship or Space Cracken best.

Thus, the correct choices are B and D.