Final answer:
To estimate the proportion of the voting population that prefers Candidate A, use the sample proportion as an estimate and calculate the confidence interval. For this sample, the confidence interval is (0.465, 0.655), meaning we can be 95% confident that the true proportion falls within this range.
Step-by-step explanation:
To estimate the proportion of the voting population that prefers Candidate A, we can use the sample proportion as an estimate. In this case, 56 out of 100 people preferred Candidate A, so the sample proportion is 56/100 = 0.56.
To calculate the confidence interval, we can use the formula: Sample proportion +/- Margin of error. The margin of error can be calculated using the formula: z * sqrt((sample proportion * (1 - sample proportion)) / sample size).
For a 95% confidence interval, the z-value is approximately 1.96. Plugging in the values, we get:
0.56 +/- 1.96 * sqrt((0.56 * (1 - 0.56)) / 100) = 0.56 +/- 0.095
The confidence interval is therefore (0.465, 0.655), which means we can be 95% confident that the true proportion of the voting population that prefers Candidate A falls within this interval.