I have been given a problem for homework with which I need a little help. In part A, I suspect that the solution has to do something with the degrees of freedom where we use n-1 for sample and n for population when calculating the standard deviation, but I do not like the idea of estimating for population. Is it not an extrapolation? Furthermore since we are not given the sum of x^2, how would you compute the standard deviation? In part B, since we have found the standard deviation of population in part A, would you use t-distribution or normal distribution? I am asking especially because the standard deviation of the population will already be an estimation. I appreciate your kind help! The problem is following:
Michael regularly buys 150g packets of tea. He has noticed recently that he gets more cups of tea than usual out of one packet, and suspects that the packets contain more than 150g on average. He weighs eight packets and finds that their mean mass is 153g and the standard deviation of their masses is 4.2g.
A) Find the unbiased estimate of the standard deviation of the mass based on Michael´s sample.
B) Assuming that the masses are normally distributed, test Michael´s suspicion at 5% level of significance.