A consumer advocacy group suspects that a local supermarket's 250-gram packages of cheddar cheese actually weigh less than 250 grams. The group took a random sample of 20 such packages and found that the mean weight for the sample was 248.875 grams. The population follows a normal distribution with the population standard deviation of 3.75 grams. You are asked to perform a hypothesis test to confirm the suspection from the consumer advocacy group.

a. State your null and altenative hypothesis. (5 marks)

b. Test your hypothesis with a significance level 0.01. (15 marks)

c. What is your conclusion? (5 marks)