In a city of 72,500 people, a simple random sample of four households is selected from the 25,000 households in the population to estimate the average cost on food per household for a week. The first household in the sample had 4 people and spent a total of $150 in food that week. The second household had 2 people and spent $100. The third, with 4 people, spent $200. The fourth, with 3 people, spent $140.
(a) Identify the sampling units, the variable of interest, and any auxiliary information associated with the units
(b) Describe two types of estimators for estimating the mean expenditure per household for a week's food in the city. Summarize some properties of each estimator.
(c) Estimate mean expenditure using the first estimator, and estimate the variance of the estimator.
(d) Estimate mean expenditure using the other estimator, and estimate the variance of the estimator. (e) Based on the data, which estimator appears preferable in this situation?