The game Settlers of Catan is a game of expansion and resource collection. To collect resources players roll two die and use the sum of the die to determine which resource they should pick up. In playing this game, it is inevitable that people complain that the die aren't fair. From n=363n=363 rolls of the die, the following empirical data were obtained: Sum of die 2 - 4 5 - 6 7 8 - 9 10 - 12 Number of times rolled 50 82 57 99 75 In order for the die to be fair, the probability of observing each sum should be Sum of die 2 - 4 5 - 6 7 8 - 9 10 - 12 Probability 6/36 9/36 6/36 9/36 6/36 At the 5% significance level, do the observed data provide sufficient evidence to conclude that the die in question are not fair?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The game Settlers of Catan is a game of expansion and resource collection. To collect resources players roll two die and use the sum of the die to determine which resource they should pick up. In playing this game, it is inevitable that people complain that the die aren't fair. From n=363n=363 rolls of the die, the following empirical data were obtained:
| Sum of die | 2 - 4 | 5 - 6 | 7 | 8 - 9 | 10 - 12 |
|---|---|---|---|---|---|
| Number of times rolled | 50 | 82 | 57 | 99 | 75 |
In order for the die to be fair, the
| Sum of die | 2 - 4 | 5 - 6 | 7 | 8 - 9 | 10 - 12 |
|---|---|---|---|---|---|
| Probability | 6/36 | 9/36 | 6/36 | 9/36 | 6/36 |
At the 5% significance level, do the observed data provide sufficient evidence to conclude that the die in question are not fair?
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