In a survey of 314 registered voters, 156 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)0.450, 0.543)
B)(0.469, 0.525)
C)(0.441, 0.552)
D)(0.388, 0.605)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the proportion of registered voters who want to see Mayor Waffleskate defeated, we use the formula for a confidence interval for a proportion: $$p \pm z*\sqrt{\frac{p(1-p)}{n}}$$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the desired confidence level (for 95%, $z = 1.96$), and $n$ is the sample size. Here, $p = \frac{156}{314}$, and $n = 314$. Plugging these values into the formula gives us the interval (0.441, 0.552).

In a Survey of 314 Registered Voters, 156 of Them