1. List all possible simple random samples of size n=2 that can be selevted from the population (0,1,2,3,4,). Calculate o^2 for the population and V(y with a bar over the y) for the sample.
2. For the simple random samples generaed in the previous question calculate s^2 for each sample. Show numerically that
3. A simple random sample of 100 water metes within a community is monitored to estimate the average daily water consumption per houseold over a specified dry spell. The sample mean and sample variance are found to be mean 12.5 and sd 1252. Estimate the total number of gallons of water, t, used daily during the dry spell. Place a boud on the error of estimation.
For #1, you can list all possible pairs (0,1), (0,2)...(3,4). I assume sampling without replacement. sigma^2 for the population can be calculated using the formula for std. dev. For variance of ybar, you calculate the eman from each ample, then apply the formula for sd.
For #2 you follow the definition of s^2 and sigma^2. It should be straightforward.