We are monitoring the performance of a network using several KPI's. We want to detect if there are any anomalies for a KPI X within last hour for which we obtained (usually) 30 values from the last hour. We don't know the population standard deviation BUT we can calculate the standard deviation for the KPI X from day zero (when the monitoring was first started).
My first question is if I calculate the standard deviation for the KPI X from day zero will that be the population's standard deviation ?
And secondly which test is more reliable and appropriate for a situation like this ? I am thinking like t-test is the way to go but sometimes we can 600 values per hour so I am not sure if t-test is suitable for such a large amount of values.