An aquarium manager wants to study gift shop browsing. she randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. she randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit. find the lower bound of the 95% confidence interval for the difference in population proportions of couples with children that enter the gift shop and couples without children that enter the gift shop. let the couples with children be sample 1 and let the couples without children be sample 2. assume that the samples are independent. enter your answer as a decimal rounded to three decimal places.