Suppose that all residencies in a small town can be categorized as 3500 houses, 4500 apartments, and 1000 condominiums.

a. (2 marks) You believe that , where index 1 represents houses, index 2 apartments and index 3 condominiums. How would you allocate a stratified sample of 900 observations if you wanted to estimate the mean electricity consumption for all households in the city?

b. (2 marks) Assume that 45% of house residents, 25% of apartment residents, and 3% of condominium residents practice energy conservation. Give an estimate for the proportion of residents practicing energy conservation.

c.( 2 marks) Let be the proportion obtained if simple random sampling was used. Compare the variances of and and give an explanation of the observed relationship.