A survey was given and here are the results "Number responding less than 1 week"

Gender - X N

Males - 71 411

Females - 64 253

a) Construct a 95% confidence interval for the difference in the proportions of males and females at this university. Who would respond less than one week?

b) does there appear to be evidence of a difference in the proportions of men and women at this university who would respond less than 1 week. Provide statistical justification

P2 = 71/411 = 0.1727

p1 = 64/253 = 0.2530

(p1 - p2) = 0.2530 - 0.1727 = 0.0803

SE = sqrt{[p1 (1 - p1) / n1] + [p2 (1 - p2) / n2]} = sqrt{[0.2530 (1 - 0.2530) / 253] + [0.1727 (1 - 0.1727) / 411]} = sqrt (0.000747 + 0.0003476) = sqrt (0.001095) = 0.0331

Therefore, 95% confidence interval for the difference in the proportions of males and females at this university who would respond less than one week = (p1 - p2) + or - 1.96 (SE) = 0.0803 + or - 1.96 (0.0331) = 0.0803 - 0.0648 to 0.0803 + 0.0648 = 0.0155 to 0.1451

b.) Yes.