Question

Q2 - Expected and observed frequencies

It is beleived that a 6-sided dice is biased so that:

If you roll the dice 360 times, what is the expected frequency for each score?

P(1) = 0.1 P(2) = 0.15 P(3)= 0.05 P(4) = 0.2
P(5) = 0.2 P(6) = 0.3


Score | 1 2 3 4 5 6
expect| ***6 boxes are here**
-ed |
frenqu|
-ency |

—————————

In fact the observed frequencies are as follows:

Score 1. 2. 3. 4. 5. 6
Observed. 39 59. 17. 71. 78. 96
frequency

What does this tell you?
1. the model seems reasonable
2. the model is wrong
3. you need to buy a new dice

Answer 1

1 and 3. For 1, look below. You really do need to buy new dice.

Explanation:

For the sake of simplicity let's turn all these decimals to ratios.

Divide all by 0.05, then let's add the observed frequency on top. Then we can divide the big number by the small one.

2 - 39: 20

3 - 59: 20

1 - 17: 17

4 - 71: 18

4 - 78: 20

6 - 90: 15

It's up to you to decide if the model is reasonable. To me, it is.