Answer
a)0.54
b)0.0201
c)p is between 0.54-0.0201=0.5199 and 0.54+0.0201=0.5601.
d)We are 80% sure that p is between 0.5199 and 0.5601.
Work Step by Step
a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{543}{1005}=0.54.$
b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=2.575\cdot \sqrt{\frac{0.54\cdot (1-0.54)}{1005}}=0.0201.$
c) Confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.54-0.0201=0.5199 and 0.54+0.0201=0.5601.
d)We are 80% sure that p is between 0.5199 and 0.5601.
