Question

A poll of 826 students at alpha statue college found that 61% of those polled preferred a quarter system to a trimester system estimate a 95% confidence interval for the percentage of students who prefer a quarter system

Answer 1

To find the confidence interval, we use the following formula.

$p\pm z\cdot\sqrt[]{\frac{p(1-p)}{n}}$

Where z = 1.96 for a 95% confidence interval. Replacing the given information, we have the following:

$\begin{gathered} 0.61\pm1.96\cdot\sqrt[]{\frac{0.61(1-0.61)}{826}} \\ 0.61\pm1.96\cdot\sqrt[]{\frac{0.61(0.39)}{826}} \\ 0.61\pm1.96\cdot\sqrt[]{\frac{0.24}{826}} \\ 0.61\pm0.03 \end{gathered}$

So, the confidence interval is

$\begin{gathered} (0.61-0.03;0.61+0.03) \\ (0.58;0.64) \end{gathered}$

The interval: (0.58 ; 0.64)