2. An apartment building bas nine floors and each floor bas four apartments. The building owner wants to install new carpeting in eight apartments to see how well it wears before she decides whether to replace the carpet in the entire building. The figure below shows the floors of apartments in the building with their apartment numbers. Only the nine apartments indicated with an asterisk (*) have children in the apartment. 12 21 22* 31 32 1st Floor 2nd Floor 3rd Floor 14 13 24 23* 34 33 42 51* 52 61 62 * = Children 4th Floor 5th Floor 6th Floor in the 43 54 53 64 63 apartment 71 72 81 82 91 92% 7th Floor 8th Floor 9th Floor 74* 73" 84* 83 94 93* (a) For convenience, the apartment building owner wants to use a cluster sampling method, in which the floors are clusters, to select the eight apartments. Describe a process for randomly selecting eight different apartments using this method. (b) An alternative sampling method would be to select a stratified random sample of eight apartments, where the strata are apartments with children might include two randomly selected apartments with children and six randomly selected apartments with no children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as opposed to a cluster sample of eight partments using the floors as clusters. 41 44