Here is a problem about sampling.

2. [24 points] A wheat farmer cuts down the stalks of wheat and gathers them in 200 piles. The 200 gathered piles will be put on a truck. The truck goes to a large flour manufacturer who will separate the grain kernels from the stalks, and just pay the farmer for the grain. The farmer wants to estimate the total weight of grain on the field, and draws a simple random sample of 5 piles from the 200 piles on the field. For each pile sampled the farmer weighs the pile, then separates the grain kernels from the stalks, and weighs the grain kernels. The sample data are as follows (weight is in lbs). Pile 1 Pile 2 Pile 3 Pile 4 Pile 5 Weight of pile 30 40 50 60 45 Weight of grain in pile 3.2 4.2 4.5 5.9 4.7 1) [4 points] Estimate the total weight of grain in all 200 piles. 2) [4 points] Give a bound on the error of estimation in Question 1).3) [4 points] The truck is weighed before and after loading, and the total weight of the 200 piles is found to be 8900 pounds. With this additional information, estimate the total weight of grain in all 200 piles using the ratio estimator. 4) [4 points] Give a bound on the error of estimation in Question 3).5) [4 points] With the additional information in Question 3), estimate the total weight of grain in all 200 piles using the regression estimator. 6) [4 points] Give a bound on the error of estimation in Question 5)