Step 1 :The question is asking for a 95% confidence interval for the proportion of adult residents who are parents in a certain county. The sample size is 300 and the number of successes (adults who are parents) is 234.
Step 2 :The formula for a confidence interval for a proportion is given by: \(\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\) where \(\hat{p}\) is the sample proportion, Z is the Z-score corresponding to the desired level of confidence, and n is the sample size.
Step 3 :In this case, \(\hat{p} = \frac{234}{300}\), Z = 1.96 (for a 95% confidence interval), and n = 300.
Step 4 :We can plug these values into the formula to find the confidence interval.
Step 5 :Calculate the standard error (SE) using the formula \(SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\) which gives SE = 0.0239.
Step 6 :Calculate the lower and upper bounds of the confidence interval using the formula \(\hat{p} \pm Z \times SE\) which gives CI_lower = 0.733 and CI_upper = 0.827.
Step 7 :The 95% confidence interval for the proportion of adult residents who are parents in this county is \(\boxed{[0.733, 0.827]}\).