A consumer group claims that a confectionary company is placing less than the advertised amount in bags of candies labelled as weighing an average of 500 grams. The consumer group takes a random sample of 25 bags of this candy, empties the contents, and finds an average weight of 485 grams. Assume the population standard deviation is known to be 12 grams. Further, assume that the conditions are satisfied and do NOT need to be checked. Test at 10% 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, with your reasoning.

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