Answer
The Gallup’s headline is correct.
Work Step by Step
The null and alternative hypotheses are as follows:
\[{{H}_{0}}:p=0.5\]
and
\[{{H}_{1}}:p>0.5\]
\[100\left( 1-\alpha \right)%\] CI for proportion is
\[\begin{align}
& \hat{p}\pm z{{\sigma }_{p}}=\hat{p}\pm E \\
& =0.55\pm 0.03 \\
& =0.52\text{ to 0}\text{.58}
\end{align}\]
The population proportion p that does not drop in the CI proportion is 0.52 to 0.58. Hence, H0 is rejected. Thus, the Gallup’s headline is correct.
