From a city of 120,000 residents, 2,400 were selected at random and questioned about a new city park initiative. Based on the poll, it is believed that 45% of the residents in the city support the initiative, with an associated margin of error of 4%. Based on these findings, which of the following is a plausible value for the total number of residents in the city who support the new city park initiative?
Question
From a city of 120,000 residents, 2,400 were selected at random and questioned about a new city park initiative. Based on the poll, it is believed that 45% of the residents in the city support the initiative, with an associated margin of error of 4%. Based on these findings, which of the following is a plausible value for the total number of residents in the city who support the new city park initiative?
Solution
The poll suggests that 45% of the residents support the initiative, but there is a margin of error of 4%. This means the actual percentage of residents who support the initiative could be as low as 41% (45% - 4%) or as high as 49% (45% + 4%).
To find the plausible number of residents who support the initiative, we need to calculate these percentages of the total population of the city.
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Calculate the lower bound: 41% of 120,000 residents 0.41 * 120,000 = 49,200 residents
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Calculate the upper bound: 49% of 120,000 residents 0.49 * 120,000 = 58,800 residents
So, based on the poll and the associated margin of error, a plausible value for the total number of residents in the city who support the new city park initiative could be anywhere between 49,200 and 58,800.
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