A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design? (A) Send a survey to all city residents and use the first 500 returned surveys for the sample. (B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained. (C) Select one voting district at random, and then select a random sample of 500 from the selected voting district. (D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district. (E) Select the first 500 city residents who attend the next high school football game.

Question

Mathematics

Kristen Avery

5 March, 16:22

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design? (A) Send a survey to all city residents and use the first 500 returned surveys for the sample. (B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained. (C) Select one voting district at random, and then select a random sample of 500 from the selected voting district. (D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district. (E) Select the first 500 city residents who attend the next high school football game.

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Answers (1)

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Kelsie Bond · Answer 1

Option B

Step-by-step explanation:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)