Answer
a)50.99%
b)p is between 46.84% and 55.14%.
c)No.
Work Step by Step
a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{284}{557}=0.5099=50.99$%.
b)$\alpha=1-0.95=0.05.$
$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.95\cdot \sqrt{\frac{0.5099\cdot (1-0.5099)}{557}}=0.0415=4.15$%
Hence the confidence interval:p is between 50.99%-4.15%=46.84% and 50.99%+4.15%=55.14%.
c) The confidence interval counted in b) contains 50% and values lower than 50%, hence the answer is no.
