Final answer:
To find the 95% confidence interval for the voter's preference towards a candidate, you calculate the margin of error using the z-score for 95% confidence, the sample proportion, and the sample size, and then add and subtract it from the sample proportion.
Step-by-step explanation:
You've asked about finding the 95% confidence interval for the proportion of voters in favor of a particular candidate based on a sample poll. In this case, you have a sample size of 400 voters with 58% in favor of the candidate. The confidence interval will give us a range within which we can be 95% certain that the actual proportion of the population in favor falls.
To calculate the 95% confidence interval for the proportion, we would use the following formula:
- Confidence Interval = Sample Proportion ± Margin of Error
The Margin of Error (ME) can be calculated using the formula:
- ME = z * sqrt((p*(1-p))/n)
Where:
- z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence)
- p is the sample proportion (0.58 in this example)
- n is the sample size (400)
After calculating the Margin of Error, you will then add and subtract it from the sample proportion to find the lower and upper bounds of the confidence interval.