Lets say we are rolling 2 dice of different sides. Example: Dice 1 has 128 sides and Dice 2 has 256 sides.
I created a 2D array of size 128X256 to bin the result of dice1,dice2 combination. If it is 0,0 I increment location 0. If it is 0,1 I increment location 1 and so on.
I also keep account of the average. Example if. it is 0,0 average is 0 & I keep track of how many times that average occurred. & if it is 0,1 average is 0.5 and so on.
With a single trial of N iterations, I got the following :
For the bins : Minimum value : 806 Maximum value : 60907 Mean : 1831.054688 Standard Deviation : 1356.090617 Median : 1541 Variance : 1838981.761
For the average: Min 0 Max 191 Mean 94.60301218 Std Dev 41.63474096 Median 95
How can I apply confidence interval on the above data?
For the average case I calculated Std Err (SE) as Std Dev/sqrt of N & then multiplied it with. z. score for 95% confidence interval (1.96)
& then specified my interval as 94.603 +- z*SE
Is this correct?
Also I did 30 such trials. Is the better way to take the mean of means of each of these samples & Then apply confidence interval on that?
My final goal is to distribute M items to each of those bins such that each bin corresponds to picking an item. Through the distribution, each item is supposed to be picked with a certain ratio. I was also thinking should I be applying confidence interval to that ratio?
Is applying z score for this case correct approach? Sorry about the long question - Its been years since I learned statistics in high school. Can't remember much :)