In order to attract a national Basketball Association (NBA) expansion team to a large city, the local government would have to agree to construct a new arena, A statistical research firm is hired to investigate support among city residents for a referendum that would raise taxes to subsidize the cost of building the new arena. Based on the differences among the voting districts within the city, the firm decides to use a stratified random sampling design 1o obrain a sample of 1000 city residents. Which of the following methods best achieves the desired sampling design? (A) Send an email survey to all city residents and use the first 1000 returned surveys for the sample. (B) Select one voting district at random, then randomly select 1000 names from the residents in the district to form the sample. (C) From an alphabetized list of all city residents, select the first 1000 residents on the list and then make sure that there is at least one resident from each district in the sample. (D) Select the first 1000 city residents who attend the local college team's next home basketball game to form the sample. (E) Select a random sample from each voting district based on the proportion of city residents in the district so that a sample of size 1000 is obtained.
Question
In order to attract a national Basketball Association (NBA) expansion team to a large city, the local government would have to agree to construct a new arena, A statistical research firm is hired to investigate support among city residents for a referendum that would raise taxes to subsidize the cost of building the new arena. Based on the differences among the voting districts within the city, the firm decides to use a stratified random sampling design 1o obrain a sample of 1000 city residents. Which of the following methods best achieves the desired sampling design? (A) Send an email survey to all city residents and use the first 1000 returned surveys for the sample. (B) Select one voting district at random, then randomly select 1000 names from the residents in the district to form the sample. (C) From an alphabetized list of all city residents, select the first 1000 residents on the list and then make sure that there is at least one resident from each district in the sample. (D) Select the first 1000 city residents who attend the local college team's next home basketball game to form the sample. (E) Select a random sample from each voting district based on the proportion of city residents in the district so that a sample of size 1000 is obtained.
Solution
The best method to achieve the desired sampling design in this scenario would be option (E) "Select a random sample from each voting district based on the proportion of city residents in the district so that a sample of size 1000 is obtained." This method ensures that each district is represented proportionally, which aligns with the stratified random sampling design. The other options either do not ensure a random or representative sample, or do not take into account the differences among the voting districts.
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