news network published the results of an exit poll conducted during a presidential election. The survey reported 15,590 total respondents. Respondents are categorized according to age-groups. Table 4 reflects the percentage distribution of respondents and the percentage of respondents from each group who voted for candidate A or candidate B.
The entries in the first column mean that 65% of the respondents who were aged 18-24 years at that time voted for candidate A and 31% chose candidate B. This led to a 4% unreported response, which could either mean that they did not cast a vote for president or they did not want to share their votes.
Table 4. Exit Poll Survey Results
Age (in years)
18–24
9%
25–29
7%
30–39
16%
40–49
16%
50–64
30%
65 or older
22%
Voted for candidate A 65%
54%
51%
54%
47%
47%
Voted for candidate B 31%
43%
46%
44%
52%
52%
Use the results of the exit poll to answer the succeeding questions.
Use above for details for this question
If 1000 more voters were surveyed, would it have been more likely to poll a 50-64 year old candidate A supporter than a 30-39 year old candidate B supporter? How can you tell?
To determine which scenario is more likely, we can calculate the number of candidate A supporters in the 50-64 age group and the number of candidate B supporters in the 30-39 age group.
For the 50-64 age group:
30% of 15,590 respondents = 4,677 respondents
47% of 4,677 respondents = 2,201 candidate A supporters
For the 30-39 age group:
16% of 15,590 respondents = 2,494 respondents
46% of 2,494 respondents = 1,147 candidate B supporters
If 1,000 more voters were surveyed, the number of respondents in each age group would increase proportionally based on the percentages provided. This means that the ratio of candidate A supporters in the 50-64 age group to all respondents would remain the same, but the actual number of candidate A supporters in that age group would increase. Similarly, the ratio of candidate B supporters in the 30-39 age group to all respondents would remain the same, but the actual number of candidate B supporters in that age group would increase as well.
Therefore, it would be more likely to poll a 50-64 year old candidate A supporter than a 30-39 year old candidate B supporter with 1,000 more voters surveyed. This is because the number of candidate A supporters in the 50-64 age group (2,201) is already higher than the number of candidate B supporters in the 30-39 age group (1,147) in the original survey results. With more voters surveyed, the number of candidate A supporters in the 50-64 age group would likely increase even further, making it more likely to poll a candidate A supporter in that age group than a candidate B supporter in the 30-39 age group.