Hi, the understanding of this problem is important to me so the
working takes priority but the overall answer is needed too. Thanks!

A company labels each pack of candy as containing 660g, but
company aims to put in an average of at least 670g to be safe. Sample
of 60 packs checked at start of each batch and if a sample is found to
contain less than 670g then production is stopped and the equipment is
adjusted. Latest batch had average contents of 666g with standard
deviation of 20g.

a) Carry out an appropriate statistical test for the latest batch (use
5% significance level and state the conclusion)

b) Using the statistical test in part a) what is the chance that the
production process is stopped to be adjusted when the batch is
actually obtaining its target average pack contents of 670g? Justify.

c) If the true mean for the batch was 658g, calculate the power of the
statistical test used in part a). What does this say about the chances
of the company misleading its customers in a particular batch without
knowing it?