A consumer group claims that a confectionary company is placing less than the advertised amount in boxes of chocolate labelled as weighing an average of 250 grams. The consumer group takes a random sample of 36 boxes of this chocolate, empties the contents, and finds an average weight of 240 grams. Assume the population standard deviation is known to be 10 grams. Further, assume that the conditions are satisfied and do NOT need to be checked. Test at the 1% level of significance.

a) Write the hypotheses to test the consumer group's claim.

b) Find the calculated test statistic.

c) Give the critical value.

d) Give your decision, explaining your reasoning.

e) Give your conclusion in the context of the claim.