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.

   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
2. 2.

   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

3. 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): -2: 6, -1: 24, 0: 40, 1: 21, 2: 7, 3: 2.

4. 3.

   Milo's class tested quiet versus music while studying, on 24 students assigned at random. The quiet-room group remembered 1 more word on average. What share of the chance dots are at 1 or more?

   0.3
5. 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?

   • It proves the coin is unfair.
   • A good fit: any result can happen by chance, even one that fair coins rarely make.
   • Not a good fit: only 2 of 100 sets reached 15, so a fair coin rarely does this.
6. 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.
   • A good fit: 25 of 100 sets reached 7 or more, so a fair number cube often does this.
   • Not a good fit: 7 sixes is too far from 5 for a fair number cube to reach by chance alone.
7. 6.

   Ren's spinner with 4 equal parts landed on red 16 times in 40 spins. The plot shows 100 sets of 40 with a fair spinner. Is a fair spinner a good model for the spinner?

   • It proves the spinner is unfair.
   • Not a good fit: only 2 of 100 sets reached 16, so a fair spinner rarely does this.
   • A good fit: any result can happen by chance, even one that fair spinners rarely make.
8. 7.

   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.
   • A good fit: 18 of 100 sets reached 7 or more, so a fair coin often does this.
   • Not a good fit: 7 heads is too far from 5 for a fair coin to reach by chance alone.
9. 8.

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

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