Use the sample data and confidence level given below to complete parts (a) through (d). In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2310 subjects randomly selected from an online group involved with ears. 1150 surveys were returned. Construct a $95 \%$ confidence interval for the proportion of returned surveys. Click the icon to view a table of $z$ scores. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.)

Step 1 ：Given that the total number of surveys sent out is 2310 and the number of returned surveys is 1150.

Step 2 ：The best point estimate of the population proportion p is the sample proportion, which is the number of successes (in this case, returned surveys) divided by the total number of trials (in this case, the total number of surveys sent out).

Step 3 ：Calculate the sample proportion (\(\hat{p}\)) as \(\frac{1150}{2310} = 0.498\).

Step 4 ：\(\boxed{\text{The best point estimate of the population proportion p is approximately 0.498.}}\)

Step 5 ：To construct a 95% confidence interval for the population proportion p, we need to use the formula for the confidence interval for a proportion, which is \(\hat{p} \pm z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\), where \(\hat{p}\) is the sample proportion, z is the z-score corresponding to the desired confidence level (for a 95% confidence level, z is approximately 1.96), and n is the sample size.

Step 6 ：Substitute the values into the formula: \(0.498 \pm 1.96*\sqrt{\frac{0.498*(1-0.498)}{2310}}\)

Step 7 ：Calculate the confidence interval to get (0.477, 0.518).

Step 8 ：\(\boxed{\text{The 95% confidence interval for the population proportion p is approximately (0.477, 0.518).}}\)