Umbrella Corporation is trying to determine whether a new drug improves mood in individuals with bipolar disorder. The company gave the drug to 253 individuals (Group 1) and a placebo (or sugar pill) to a separate sample of 285 individuals (Group 2). After one month on the drug, 178 of the patients in Group 1 reported improved mood, while 163 of the patients in Group 2 reported the same. Calculate the lower bound of a 95% confidence interval for the true difference in the proportion of individuals who experienced improved mood, to two decimal places.