I took two statistics classes at college and I remember "hypothesis testing" to be a very powerful tool if only I could apply it correctly. It seems that while I was in college solving problems, I was always given the population's standard deviation to solve the question. However, what if I want to apply it in my job (i.e. track a particular process)? How can I obtain the true standard deviation of a process?
I am interested in normally distributed data. Let's say that I work at an industry that designs sprinkles, and I was interested to know if the product meets the specifications. The sprinkles were designed so that the average activation response time should be 25 (in a fire prevention system). Let's say I analyzed the times until 10 sprinkler samples activate in response to heat, and I got 27,41,22,27,23,35,30,33,24,27 (in seconds). Now I made the hypothesis test if the mean is equal to 25 or not equal to 25.