I just want to share a problem that was shown as an example for confidence intervals that I am bit confused about. It is;
In a poll of 100 randomly selected voters, 35 of them expressed support for candidate A. We wish to estimate the proportion of voters that support candidate A from the entire population.
In the example, they wanted to use this:
$\widehat{p} \pm z_{\frac{\alpha}{2}}\cdot \left ( \sqrt{\frac{\hat{p} (1-\widehat{p})}{n}} \right)$
We are given:
confidence Interval = 95% (1.96)
$n = 100$
$\widehat{p} = \frac{35}{100}$
However, with the numbers plugged into its place, it was written like this:
${\frac{35}{100}} \pm 1.96\cdot \left ( \sqrt{\frac{{\frac{35}{100}} \cdot\frac{65}{100}}{100}} \right)$
Why was the $1-\widehat{p}$ replaced by $({\frac{35}{100}} \cdot\frac{65}{100})$ ?