In a survey of 318 registered voters, 176 of them wished to see Mayor Waffleskate lose her next election. Construct a 95% confidence interval for the proportion of registered voter who want to see Mayor Waffleskate defeated.
A) (0.526, 0.581)
B) (0.446, 0.661)
C) 0.508, 0.599)
D) (0.499, 0.608)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the proportion of registered voters who want to see Mayor Waffleskate defeated, we first calculate the sample proportion $ p = \frac{176}{318} $. Then, we use the formula for the confidence interval for a proportion: $ p \pm z \sqrt{\frac{p(1-p)}{n}} $, where $ z $ is the z-score corresponding to a 95% confidence level (approximately 1.96), $ p $ is the sample proportion, and $ n $ is the sample size. Plugging in the numbers, we get the confidence interval as approximately (0.499, 0.608).

In a Survey of 318 Registered Voters, 176 of Them