Final answer:
The 95% confidence interval for the population proportion of voters who will vote for a certain candidate is calculated using the confidence interval formula for a population proportion, yielding an interval of (32.44%, 59.56%).
Step-by-step explanation:
To determine the 95% confidence interval for the population proportion of voters who will vote for a certain candidate, when a random sample of 50 voters found that 46% were going to vote for the candidate, we use the formula for a confidence interval of a population proportion:
CI = ± z * √(p'(1-p')/n)
where CI is the confidence interval, z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence), p' is the sample proportion (0.46), and n is the sample size (50).
Plugging in the values, we get:
EBP = ± 1.96 * √(0.46(1-0.46)/50)
EBP = ± 1.96 * √(0.46*0.54/50)
EBP = ± 1.96 * 0.0692
EBP = ± 0.1356
The 95% confidence interval for the population proportion is therefore:
CI = 0.46 ± 0.1356
CI = (0.3244, 0.5956)
We can be 95% confident that the true population proportion of voters who will vote for the candidate is between 32.44% and 59.56%.