Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 971 and standard deviation of 15.2 . Propose a model for the weight of the hammers including a probability distribution for the weight. What are the assumptions for this model to hold? What parameters does this model have?

A new production system is configured, and one wants to evaluate if the new system makes more constant weights. For this a random sample of newly produced hammers is evaluated yielding the following weights:

987, 966, 955, 977, 981, 967, 975, 980, 953, 972

What hypothesis can you formulate and what test and decision rule can you make to estimate if the new system produces a more constant weight? Express these assertions as logical statements involving critical values. What error probabilities can you suggest and why? Calculate the -value. Perform the test and express conclusions.