Use a simulation to test a model, and to compare two treatments

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Jun's class tested plant food on 20 bean plants, assigned at random. The plant-food group grew 3 cm more on average. What share of the chance dots are at 3 or more?

   0.05
2. 2.

   Kira's class tested two wing designs on 24 paper airplanes, assigned at random. The long-wing planes flew 2 feet farther on average. What share of the chance dots are at 2 or more?

   0.19
3. 3.

   Luz's class tested ruler-drop practice on 20 students, assigned at random. The practice group's mean catch distance was 3 cm shorter. What share of the chance dots are at 3 or more?

   0.06
4. 4.

   Noah's coin landed heads 15 times in 20 flips. The plot shows 100 sets of 20 with a fair coin. Is a fair coin a good model for the coin?

   • Not a good fit: only 2 of 100 sets reached 15, so a fair coin rarely does this.
   • A good fit: any result can happen by chance, even one that fair coins rarely make.
   • It proves the coin is unfair.
5. 5.

   Pia's number cube showed 7 sixes in 30 rolls. The plot shows 100 sets of 30 with a fair number cube. Is a fair number cube a good model for the number cube?

   • It proves the number cube is fair.
   • Not a good fit: 7 sixes is too far from 5 for a fair number cube to reach by chance alone.
   • A good fit: 25 of 100 sets reached 7 or more, so a fair number cube often does this.
6. 6.

   Tala's coin landed heads 7 times in 10 flips. The plot shows 100 sets of 10 with a fair coin. Is a fair coin a good model for the coin?

   • It proves the coin is fair.
   • Not a good fit: 7 heads is too far from 5 for a fair coin to reach by chance alone.
   • A good fit: 18 of 100 sets reached 7 or more, so a fair coin often does this.
7. 7.

   Zee's class tested plant food on 20 bean plants, assigned at random. The plant-food group grew 4 cm more on average. Is the difference bigger than chance alone would make?

   • Yes: only 3 of 100 chance deals reached 4, so plant food likely made a difference.
   • No: chance can make any difference.
   • Yes: it proves plant food always works.

8. Read this first

   Use this

   Dot plot of 100 chance deals of the 24 results into two groups of 12 (difference in mean words remembered, quiet − music, words, rounded to the nearest 1): -3: 1, -2: 3, -1: 32, 0: 31, 1: 28, 2: 5.

9. 8.

   Ari's class tested quiet versus music while studying, on 24 students assigned at random. The quiet-room group remembered 1 more word on average. Is the difference bigger than chance alone would make?

   • No: 33 of 100 chance deals reached 1, so chance alone could explain it.
   • Yes: the quiet-room group did better, so a quiet room works for students.
   • No: it proves a quiet room makes no difference.
10. 9.

    Bo's class tested ruler-drop practice on 20 students, assigned at random. The practice group's mean catch distance was 4 cm shorter. Is the difference bigger than chance alone would make?

    • Yes: it proves practice always works.
    • Yes: only 1 of 100 chance deals reached 4, so practice likely made a difference.
    • No: chance can make any difference.

11. Use this

    Dot plot of 100 chance deals of the 24 results into two groups of 12 (difference in mean flight distance, long wings − short wings, feet, rounded to the nearest 1): -2: 6, -1: 18, 0: 37, 1: 29, 2: 9, 3: 1.

12. 10.

    Esme's class tested two wing designs on 24 paper airplanes, assigned at random. The long-wing planes flew 1 foot farther on average. Is the difference bigger than chance alone would make?

    • No: 39 of 100 chance deals reached 1, so chance alone could explain it.
    • No: it proves the long-wing design makes no difference.
    • Yes: the long-wing planes did better, so the long-wing design works better.