0.680 < p < 0.800
What is the point estimate for p, and the margin of error from which the C.I. was formed?
I am confused as to what "p̂" and "E" are equal to. Normally, I would use the population and samples sizes, but this information is not available.
Assuming that $[0.680, 0.800]$ is meant to be a symmetrical, 95% confidence interval, then:
$\hat{p} - 1.96\hat{\sigma}_p=0.680 \\ \hat{p} + 1.96\hat{\sigma}_p=0.800$
Hence, by solving simultaneously, I get $\hat{p} = 0.740$ and $\hat{\sigma}_p = 0.0306$.