The St. Lucie County Health Department needs to estimate the proportion of county residents with high blood pressure. A health department researcher found that 439 out of a random sample of 1318 county residents had high blood pressure. Determine the point estimate, $\hat{p}$ and the sample standard deviation, $s_{\hat{p}}$ Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary. \[ \begin{array}{l} \hat{p}= \\ s_{p}= \end{array} \] Using a 968 confidence level, determine the margin of error, $E$, and a confidence interval for the true proportion of all St. Lucie County residents who have high blood pressure. Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary. The margin of error is given by $E=$ A $96 \%$ confidence interval is given by

Step 1 ：The point estimate, \(\hat{p}\), is the proportion of the sample that has high blood pressure, which can be calculated by dividing the number of residents with high blood pressure by the total number of residents in the sample. In this case, \(\hat{p} = \frac{439}{1318} = 0.3331\).

Step 2 ：The sample standard deviation, \(s_{\hat{p}}\), can be calculated using the formula for the standard deviation of a proportion, which is \(\sqrt{\hat{p}(1-\hat{p})/n}\), where \(n\) is the sample size. In this case, \(s_{\hat{p}} = \sqrt{0.3331(1-0.3331)/1318} = 0.012982\).

Step 3 ：The margin of error, \(E\), can be calculated using the formula \(E=z*\sqrt{\hat{p}(1-\hat{p})/n}\), where \(z\) is the z-score corresponding to the desired confidence level. In this case, \(E = 2.0537489106318225*\sqrt{0.3331(1-0.3331)/1318} = 0.0267\).

Step 4 ：The confidence interval can then be calculated by subtracting and adding the margin of error from/to the point estimate. In this case, the confidence interval is \((0.3331 - 0.0267, 0.3331 + 0.0267) = (0.3064, 0.3597)\).

Step 5 ：Final Answer: The point estimate, \(\hat{p}\), is \(\boxed{0.3331}\). The sample standard deviation, \(s_{\hat{p}}\), is \(\boxed{0.012982}\). The margin of error, \(E\), is \(\boxed{0.0267}\). A 96% confidence interval for the true proportion of all St. Lucie County residents who have high blood pressure is \(\boxed{(0.3064, 0.3597)}\).