Step 1 :Given that 710 out of 1205 individuals who earn more than $100,000 per year believe it is morally wrong for unwed women to have children, we can calculate the proportion of these individuals as \( p1 = \frac{710}{1205} = 0.589 \)
Step 2 :Similarly, given that 693 out of 1310 individuals who earn less than $100,000 per year believe it is morally wrong for unwed women to have children, we can calculate the proportion of these individuals as \( p2 = \frac{693}{1310} = 0.529 \)
Step 3 :We can calculate the standard error (SE) using the formula \( SE = \sqrt{\frac{p1 \cdot (1 - p1)}{n1} + \frac{p2 \cdot (1 - p2)}{n2}} \), where \( n1 = 1205 \) and \( n2 = 1310 \). Substituting the given values, we get \( SE = 0.0198 \)
Step 4 :For a 95% confidence interval, the Z-score is 1.96
Step 5 :We can calculate the lower bound of the confidence interval using the formula \( CI_{lower} = (p1 - p2) - Z \cdot SE \). Substituting the given values, we get \( CI_{lower} = 0.021 \)
Step 6 :Thus, the lower bound of the 95% confidence interval for the difference in proportions is \(\boxed{0.021}\)