Question

Two individuals are running for mayor in a city. You conduct an election survey among 578 respondents a week before the election and find that 51% of the respondents prefer candidate A. Can you predict a winner? Use the 99% level. (Hint: In a two-candidate race, what percentage of the voter would the winner need? Does the confidence interval indicate that candidate A has a sure margin of victory? Remember that while the population parameter is probably in the confidence interval, it may be anywhere in the interval.)

Answer 1

Based on the survey conducted a week before the election, we can predict that candidate A will win the mayor election.

Step-by-step explanation:

To determine a winner based on the survey, we can calculate the margin of error for the proportion of respondents who prefer candidate A. Since the survey was conducted with 578 respondents and 51% prefer candidate A, we can calculate the standard error using the formula:

Standard Error = sqrt(p*(1-p)/n)

With a sample size of 578, the standard error is approximately sqrt(0.51*(1-0.51)/578) = 0.022.

To calculate the margin of error, we can multiply the standard error by the critical value:

Margin of Error = Critical Value * Standard Error

For a 99% confidence level, the critical value is approximately 2.576.

So the margin of error is approximately 2.576 * 0.022 = 0.057.

Therefore, the 99% confidence interval for the proportion of respondents who prefer candidate A is 51% +/- 0.057%, or between 50.943% and 51.057%. Since the midpoint of the confidence interval is still above 50%, we can predict that candidate A will win the election based on the survey.