You roll a six-sided die 60 times. The results are: 15 times the outcome is a 1 or a 2, 22 times the outcome is a 3 or a 4, and 23 times the outcome is a 5 or a 6. Which of the following is the appropriate calculation of chi-square on these data?
To calculate the chi-square value for these data, we first need to calculate the expected frequencies for each outcome assuming a fair six-sided die.
The total number of rolls is 60.
Therefore, the expected frequency for each outcome is 60 divided by 6 = 10.
For outcomes 1 and 2:
Observed frequency = 15
Expected frequency = 10
(15-10)^2 / 10 = 2.5
For outcomes 3 and 4:
Observed frequency = 22
Expected frequency = 10
(22-10)^2 / 10 = 14.4
For outcomes 5 and 6:
Observed frequency = 23
Expected frequency = 10
(23-10)^2 / 10 = 15.3
Now, we sum up these values:
2.5 + 14.4 + 15.3 = 32.2
Therefore, the appropriate calculation for the chi-square value on these data is 32.2.