Step 1 :Given that the sample size (n) is 2323 and the number of adults who have donated blood in the past two years (x) is 423, we can calculate the sample proportion (\(\hat{p}\)) as \(\frac{x}{n}\) = \(\frac{423}{2323}\) = 0.182.
Step 2 :The z-score corresponding to a 90% confidence level is 1.645.
Step 3 :We can calculate the standard error (se) using the formula \(se = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\) = \sqrt{\frac{0.182(1-0.182)}{2323}} = 0.008.
Step 4 :Using the formula for a confidence interval for a proportion, we can calculate the lower and upper bounds of the confidence interval as \(\hat{p} \pm Z_{\alpha/2} \times se\).
Step 5 :The lower bound of the confidence interval is \(\hat{p} - Z_{\alpha/2} \times se\) = 0.182 - 1.645 \times 0.008 = 0.169.
Step 6 :The upper bound of the confidence interval is \(\hat{p} + Z_{\alpha/2} \times se\) = 0.182 + 1.645 \times 0.008 = 0.195.
Step 7 :\(\boxed{\text{We are 90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between 0.169 and 0.195.}}\)