Final answer:
A 95% confidence interval for the proportion of likely voters in favor of Amendment 1 is calculated using the sample proportion and sample size, resulting in an interval of approximately (45.47%, 50.93%). This interval suggests that there is a 95% probability that the true proportion lies within this range.
Step-by-step explanation:
To calculate a 95% confidence interval for the proportion of likely voters that would vote in favor of Amendment 1, we can use the formula for a confidence interval for a population proportion:
CI = p ± z * √(p(1-p)/n)
Where:
- p = sample proportion (48.2% or 0.482)
- z = z-score associated with a 95% confidence level (approximately 1.96)
- n = sample size (1250)
Plugging in the values, we get:
CI = 0.482 ± 1.96 * √(0.482(1-0.482)/1250)
Calculating the margin of error:
ME = 1.96 * √(0.482*0.518/1250)
ME ≈ 1.96 * √(0.0001935096)
ME ≈ 1.96 * 0.0139141
ME ≈ 0.02730 (rounded to five decimal places)
Now we calculate the interval:
Lower bound = p - ME
Lower bound = 0.482 - 0.02730
Lower bound ≈ 0.4547
Upper bound = p + ME
Upper bound = 0.482 + 0.02730
Upper bound ≈ 0.5093
Therefore, the 95% confidence interval is approximately (0.4547, 0.5093). This interval can be interpreted to mean that we are 95% confident that the true proportion of all likely voters who would vote in favor of Amendment 1 is between 45.47% and 50.93%.