52 of 1000 registered voters intend to vote for steven Collins for mayor. What is the 95 confidence interval to describe the total percentage of registered voters who intend to vote for Steven Collins?

To calculate the 95% confidence interval for the proportion of voters intending to vote for Steven Collins, we first find the sample proportion ( p = \frac{52}{1000} = 0.052 ). The standard error (SE) is calculated using the formula ( SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.052(1-0.052)}{1000}} \approx 0.005 ). Using a z-score of 1.96 for a 95% confidence level, the margin of error is ( 1.96 \times SE \approx 0.010 ). Therefore, the 95% confidence interval is ( 0.052 \pm 0.010 ), or approximately ( (0.042, 0.062) ), which translates to a percentage range of 4.2% to 6.2%.