Rolling the Dice Greg, Josia, Emeka

The Project n Roll a six-sided dice 120 times n Use a random number generator to generate digit numbers (0-9) n Test the Null Hypothesis that each digit is equally likely to have been selected and that each side of the dice is equally likely to be rolled. n Use a 5% significance level.

Modifications to the Project n 120 rolls of the dice gives an expected value of 20 for each side of the dice n The minimum for the Chi-squared statistic to be a close approximation is 5 n We rolled the six- sided dice 30, 120, 1200, and 9000 times

The Data (30 rolls)

Data (120 rolls)

Data (1200 rolls)

Data (9000 rolls)

Data (1000 random digits)

Comparison (A) n Bar Chart of Category vs. Number of observed values for 30 dice rolls

Comparison (B) n Bar Chart of Category vs. Number of observed values for 9000 dice rolls

Chi-Squared Statistic n Compares Observed and Expected numbers when the possible outcomes are divided into mutually exclusive categories n Obviously the Chi-squared statistic might reject the null hypothesis if there are too few rolls, even though a six-sided dice has equal probability of each side coming up.

Results

n We cannot reject the null hypothesis at the 5% level that each side of the dice has an equal probability of being rolled. n We cannot reject the null hypothesis at the 5% level that each digit has an equal probability of being selected.

Results n The more rolls of the dice, or the more trials of the test that we do, the more confident we can be when we reject or do not reject the null hypothesis when using the Chi- squared statistic to analyze our results.

Results n The more degrees of freedom that the test has, the more trials will be needed. This is because as the degrees of freedom increases the “expected” values go down.