## Some probability questions

Hi,

I would be grateful if anyone help me with those three questions. I need them until Monday. Many thanks in advance for those who want to help me.

1- We would like to see if a cluster sample from the rural areas of Stephens County can improve om the precision of an SRS of size 100 while costing the same. To de this, we need to know the cost of sampling 100 houses in districts 1 through 43. Use ADDGEN to generate 10 diffrent SRS of size 100 from the rural districts, calculate how much each of the cost of sampling 100 houses randomly in districts 1 through 43?
2- Design a two-stage cluster sampling scheme for the rural areas (districts 1-43 of Stephens County. Your design should (a) choose between 25 and 50% of the districts (clusters) with equal proability, (b) subsample within each chosen district with sample size proportional to district size (number of houses), and (c) cost about the same amount as an SRS of size 100.
3- Using your sample form Exercise 2, estimate the average price a rural household is willing to pay for cable TV, using both an unbiased estimate and a ratio estimate. Be sure to give standard errors and to plot the data appropriately