A university wants to determine whether a recently hired instructor is working out. Twenty-three out of 30 of Instructor A's students passed a certain test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Find the lower limit of the 98% confidence interval that can be used to test if Instructor A's success rate is worse than Instructor

NOTE: DO NOT ROUND OFF IN YOUR CALCULATIONS, ONLY PART ANSWERS AND THE FINAL ANSWER SHOULD BE ROUNDED OF TO 4 DECIMAL PLACES