Two detergents were tested for their ability to remove stains of a certain type.An inspector judged the first one to be successful on 63 out of 91 independent trials and the second one to be successful on 42 out of 79 independent trials.

a)Find a 90% confidence interval for the difference in success rates between the two detergents.Be sure to show work. (9 points)

b)Find a 98% confidence interval instead. Be sure to show work. (3 points)