8 hours sleep group (X)57535339
4 hours sleep group (Y)81466412
When given a data set one of the most important evaluations is to determine if the data set size is big enough to show relevance. So, the first thing I did was to check if the size warranted further review. Finding the smallest relevant size of data is as simple as taking the confidence quotient and multiplying this by the standard deviation to the second power. Taking this sum and dividing by .6 of the standard deviation. Another word for standard deviation is sigma and from this point forward I will use S to represent a population’s sigma and s to represent a sample set sigma. In this situation, the first data set equation looks like:
The second data set returned 8.37 because the sigma for the second data set was bigger than the first. Both of these numbers need to be rounded up to the nearest whole number and then compared to the sample size. The first sample set is equal to the recommended smallest sample size however the second sample size falls short by one datum. This test leads me to believe that the sample sizes are not big enough to stand up to significant scrutiny. Be that as it may, the data was put into a distribution chart to compare the distribution patterns to see any significant difference however, there was no significant difference. The next step to finding if there was a change between the samplings was to test the sigmas in an f test. This test takes the larger sigma squared and divides by the smaller sigma squared to create f. Then compares the number of datum in the sample to an f chart that gives a range of numbers and if the f falls between the range specified for the number of datum in the sample then the sigmas are not significantly different. This test shows that there is not a 95% probability that the samplings are significantly different and therefore does not support Sam’s theory. Taking this to the next statistical significance test takes us to a t test. To be specific, the test used in this comparison is the t test of two sample averages. However, this equation gets a little complicated for words so, it is best to illustrate this computation. Before doing so we need to establish some symbology for each of the numbers. 1 = the mean of group X2 = the mean of group Y n1 = the number of datum in group X n2 = the number of datum in...