A machine is set-up to fill bags of ground coffee with an average weight of 150 grams. Assume the population standard deviation is known to be 5 grams. The machine operator believes that the machine is over filling the bags. She takes a random sample of 30 bags of ground coffee, finding a mean weight of 158 grams. Assume the conditions are satisfied.

a) Write the hypotheses to test the machine operator's belief.

b) Find the calculated test statistic. SHOW BASIC WORKINGS.

c) If testing at the 10% level of significance, give the critical value.

d) Give your DECISION, briefly explaining your reasoning.

e) Give your CONCLUSION, briefly explain your reasoning.

f) Describe a Type I error in the context of this question.