2. REASON QUANTITATIVELY A local television station reports that a sample poll indicated that \( 46 \% \) to \( 58 \% \) of the registered voters in a city plan to vote for Candidate A. a. What is the sample mean of the population? What does this mean? b. What is the margin of error? What does this mean? c. How many registered voters were in the sample? d. How can the television station reduce the margin of error to be more confident in applying the sample mean to the population of registered voters? der
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Given that a sample poll indicates that 46% to 58% of registered voters in a city plan to vote for Candidate A, let's dive into the concepts that underlie this data. The sample mean of the population can be calculated as the midpoint of the interval given: \((46\% + 58\%) / 2 = 52\%\). This means that, based on the sample data, it is estimated that 52% of voters favor Candidate A, giving an insight into the candidate's potential support and influencing campaign strategies. The margin of error can be found by taking half the distance between the upper and lower bounds of the poll: \((58\% - 46\%) / 2 = 6\%\). This means that the actual support for Candidate A in the entire voter population could realistically vary by plus or minus 6%, indicating a range of interest that helps to account for sampling error in predictions.