A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. Identify the sampling methods described below, and comment on whether or not you think they would be effective in this setting.
(a) Randomly sample 50 households from the city.
(b) Divide the city into neighborhoods, and sample 20 households from each neighborhood.
(c) Divide the city into neighborhoods, randomly sample 10 neighborhoods, and sample all house-holds from those neighborhoods.
(d) Divide the city into neighborhoods, randomly sample 10 neighborhoods, and then randomly sample 20 households from those neighborhoods.
(e) Sample the 200 households closest to the city council oces.

The city is first divided into the various distinct and unique neighbourhoods, then randomly sample 10 neighborhood such that this sample is a representation of the many distinct and unique neighborhoods, which include some with large homes, some with only apartments, and others a diverse mixture of housing structures.

Then from each neighborhood, take a random sample of 20 households.

This way, your sample are a representation of the population.