Question

a political campaign wants to estimate the number of adult residents who voted in the last city election. answer the following.
(a) which of the following surveys probably would best represent the entire adult population of
the city?
25 senior residents are randomly selected; 16 voted in the last election.
25 homeowners are randomly selected; 11 voted in the last election.
25 adult residents are randomly selected from the city; 10 voted in the last election.
(b) there are 21,400 adults who live in the city. using your answer from part (a), estimate the
number of adults who voted in the last city election.
adults

Explanation:

Step1: Calculate the proportion of voters in each sample

• For the sample of 25 adult residents: Proportion = $\frac{10}{25}=0.4$
• For the sample of 25 homeowners: Proportion = $\frac{11}{25}=0.44$
• For the sample of 25 senior residents: Proportion = $\frac{16}{25}=0.64$

Step2: Analyze the representativeness of each sample

• A sample of adult residents is more likely to represent the entire adult population of the city compared to samples of homeowners (a subset of adults with specific property - related characteristics) or senior residents (a subset based on age).

Step3: Estimate the number of adult voters

• If we assume the proportion of voters in the sample of adult residents ($0.4$) is representative.
• Given there are 21400 adults, the estimated number of adult voters is $21400\times0.4 = 8560$

Answer:

(a) The sample of 25 adult residents probably best represents the entire adult population of the city.
(b) $8560$