A small town contains a total of 1,800 households. The town is divided into three districts, containing 820, 540, and 440 households, respectively. A stratified random sample of 300 households contains 120, 90, and 90 households, respectively, from these three districts. Sample members were asked to estimate their total energy bills for the winter months. The respective sample means were $290, $352, and $427, and the respective sample standard deviations were $47, $61, and $93.
a. Use an unbiased estimation procedure to estimate the mean winter energy bill for all households in this town.
b. Use an unbiased estimation procedure to find an estimate of the variance of the estimator of part a.
c. Find a 95% confidence interval for the population mean winter energy bill for households in this town.