Answer
$σ_{p̂} = 0.024$
Work Step by Step
Here we have: n = 300, p = 0.224
Verifying model requirements:
a. np(1-p) = 300 x 0.224 (1 - 0.224) = 52.147 > 10
b. n is less than 5% of about 300 million US citizens.
Hence, p̂ is normally distributed.
$ μ_{p̂} = p = 0.224$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n} = \sqrt \frac{0.224(1-0.224)}{300} = 0.024$
