A local farmer produces hay for nearby cattle ranchers. The hay is rolled into 50 lb (22 kg) bales and is sold by quantity. Therefore, when a rancher buys 100 bales of hay, they can expect to receive 5,000 lbs of hay. To ensure the cattle ranchers are getting what they expect, the farmer periodically samples batches of 30 hay bales to test that they are averaging 50 lbs. The most recent batch provided a sample weight of x = 49.1 lbs. The population standard deviation is known to be σ = 3.37. Using a level of significance of α = 0.05, test to determine whether the farmer is producing what the ranchers are expecting. a) Formulate the null and alternative hypotheses. Justify your formulation. b) Calculate the test statistic. c) Use the p-value approach to draw your conclusion. d) Verify your conclusion using the critical value approach. e) Interpret your conclusion.