Save A poll conducted by the UC Berkeley Institute of Governmental Studies in 2019 found that $52.3 \%$ of 4527 respondents said they considered moving out of the state. Complete parts a through c. a) Compute a $95 \%$ confidence interval for the proportion of all Californians who considered moving out of state. $\%$ (Type intêgers or decimals rounded to one decimal place as needed.)

Step 1 ：Given that the sample proportion (\(\hat{p}\)) is 0.523 and the sample size (\(n\)) is 4527, we want to compute a 95% confidence interval for the proportion of all Californians who considered moving out of state.

Step 2 ：The formula for the confidence interval for a proportion is given by \(\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\), where \(Z\) is the Z-score corresponding to the desired confidence level. For a 95% confidence level, \(Z \approx 1.96\).

Step 3 ：Substituting the given values into the formula, we get \(0.523 \pm 1.96 \sqrt{\frac{0.523(1-0.523)}{4527}}\).

Step 4 ：Calculating the above expression, we get the 95% confidence interval as approximately [0.508, 0.538].

Step 5 ：\(\boxed{\text{Final Answer: The 95% confidence interval for the proportion of all Californians who considered moving out of state is approximately [0.508, 0.538]. This means we are 95% confident that the true proportion of all Californians who considered moving out of state lies between 50.8% and 53.8%.}}\)