I have the electronic record of my time sheets at my work, for a two year period. Every day when I reach and leave the factory, I swipe my identity card through a machine which records the time.
I generally reach work at 8.00 am, sometimes early, sometimes late. I wish to know if I am a punctual person, statistically ? on average, do I reach the office at 8.00 am or before?
I have about 500 data points. I am thinking of the following three approaches. I am not sure which one is the best.
1. Take a simple average of all the 500 arrival times. The average will tell me if I am punctual.
2. Take a sample of 50 data points, calculate the sample mean, calculate the sample variance and estimate the population variance. Assume that the population mean is 8.00 am. And see if the sample mean is within 3 standard deviations (population?s SD) from the population mean.
3. Treat the 500 data points as a sample and follow the steps outlined in the #2 approach.