Random Number Research the Population

¶ … Random Number Research

The population size is very easy to determine -- the table has ten columns and fifty rows, and thus five-hundred (fifty multiplied by ten) items in the table. The data population is thus five hundred. With this known population size, a standard sample size table can be consulted to determine an appropriate sample size based on the desired confidence interval and margin of error. For a ninety-five percent confidence interval and a five percent margin of error -- the lowest level of confidence and margin generally accepted in most instances, though lower levels of confidence and higher margins of error would not necessarily be unsuitable in this application -- a sample of two hundred and seventeen items is required.

This sample size is already high enough to serve as a reasonable enough assessment of the probability of finding a number with double digits in the overall population. For a ninety-nine degree confidence interval and a 1% margin of error, the most certain measure of probability represented in a standard sample size table, the sample size in a population of five hundred would need to be four hundred and eighty-five; at this point it would make more sense to achieve total certainty and simply assess the other fifteen items -- the full data population, in other words. Even changing to a ninety-five percent confidence interval and keeping a one-percent margin of error only drops the necessary sample size by ten items, to four hundred and seventy five, which again is so close to the total population as to make it more worthwhile to achieve one hundred percent confidence and a complete absence of any margin of error by assessing the entire population; an assessment of 217 items is still quite valid.

A fishbowl draw (or a similar method of physically randomizing the selection of numbers from the population contained in the table, such as dropping a coin from high above an enlarged version of the table and allowing it to bounce onto selected numbers) would be preferred for this study. This means of selection would fully randomize the selection, ensuring the validity of the sample, while at the same time would be fairly easy to accomplish. The creation or utilization of a computer program to randomly select numbers form this population would also be a highly valid and reliable way of accomplishing the necessary sampling, but this would be much more time-intensive as it would require the inputting of the entire population into the computer before the sample could be created. Analysis would be accomplished much faster by the computer after the data had been input, of course, but the data can be essentially analyzed (in terms of categorization at the very least) at the same time as selection in the physical randomization method.