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The confidence interval for p is\(0.0434 < p < 0.217\)

Formula for sample proportion is:

\(\hat p = \frac{{{\rm{upper confidence limit}} + {\rm{lower confidence limit}}}}{2}\)

From the given confidence interval, thelower confidence limit is 0.0434 and the upper confidence limit is 0.217.

Substituting values,

\(\begin{aligned}{c}\hat p = \frac{{0.217 + 0.0434}}{2}\\ = 0.1302\end{aligned}\)

Hence, the sample proportion is 0.130.

Formula for margin of error is:

\(\begin{aligned}{c}E = \frac{{{\rm{upper confidence limit}} - {\rm{lower confidence limit}}}}{2}\\ = \frac{{0.217 - 0.0434}}{2}\\ = 0.0868\end{aligned}\)

Hence, the margin of error is 0.087.

The confidence interval in the form of\(\hat p \pm E\)is given as:

\(\begin{aligned}{c}\hat p - E < p < \hat p + E\\0.1302 - 0.0868 < p < 0.1302 + 0.0868\\0.0434 < p < 0.217\end{aligned}\)

Therefore, the confidence interval in the form of \(\hat p{\rm{ }} \pm {\rm{ }}E\)is\(0.1302 \pm 0.0868\).