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The research group asked the following question of individuals who eamed in excess of $\$ 100,000$ per year and those who earned less than $\$ 100,000$ per year: "Do you believe that it is morally wrong for unwed women to have children? Of the 1,205 individuals who earned in excess of $\$ 100,000$ per year, 710 said yes; of the 1,310 individuals who eamed less than $\$ 100,000$ per year, 693 said yes. Construct a $95 \%$ confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.

The lower bound is $\square$ (Round to three decimal places as needed )
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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 \(\boxed{0.021}\)