A College Alumni Fund Appeals for Donations by Phoning or Emailing

Multiple Choice

A college alumni fund appeals for donations by phoning or emailing recent graduates. A random sample of 300 alumni shows that 40% of the 150 who were contacted by telephone actually made contributions compared to only 30% of the 150 who received email requests. Which formula calculates the 98% confidence interval for the difference in the proportions of alumni who may make donations if contacted by phone or by email?

A) $(0.40-0.30) +7.33 \sqrt{\frac{(0.40) (0.60) }{300}+\frac{(0.30) (0.70) }{300}}$
B) $(0.40-0.30) \pm 2.33 \sqrt{\frac{(0.35) (0.65) }{300}}$
C) $(0.40-0.30) \pm 2.33 \sqrt{\frac{(0.35) (0.65) }{150}}$
D) $0.40-0.30) +7.33 \sqrt{\frac{(0.40) (0.60) }{150}+\frac{(0.30) (0.70) }{150}}$
E) $(0.40-0.30) +2.33 \sqrt{\frac{(0.35) (0.65) }{150}+\frac{(0.35) (0.65) }{150}}$