Question

We know that the average quantity of liquid filled per bottle on a line
production is 20ml. Inaccurate filling significantly increases the
costs and in this case, the production line must be stopped and regulated. The
past experiences show that the liquid filling process follows
a normal law and the standard deviation of the liquid filled per bottle is 0.6ml. A
quality controller takes a sample of 36 bottles and must take a
decision to stop the line.
a) Formulate the hypothesis test corresponding to the controller's decision.
b) For a threshold of 1%, give the controller decision rule. Do a
graphic illustration of critical regions.
c) If the controller finds an average of 21.02 ml, what decision should he
take ?
d) If the controller finds an average of 19.14ml, what decision should he
take ?
e) The controller decides to take a sample of 100 bottles and again finds an average of 19.14ml. Should he change his decision by
compared to (d)

Answer 1