Evaluation and Control

Question

Prove the following:

1- if det(A)=0 , then AB is singular . 

2- if A and B are invertible then AB is invertible . with (AB)^-1 = B^-1 A^-1

3- if A is invertible and B , C are inverses of A , the B=C . 

4- if A is invertible then det (A^-1)= 1/det (A) .

Question

Trying to fight drug resistant bacteria a researcher tries an experimental drug on infected subjects. Out of 70 monkeys 42 showed improvements 22 got worse and 6 showed no change. Is this researcher working in the right direction? Is there a significant effect of the drug on the infection? Use two tailed test at .05

Question

A researcher would like to determine whether people really can tell the difference between bottled water and tap water. Participants are asked to taste two unlabeled glasses of water one bottled and one tap and identify the one they thought tasted better. Out of 40 people in the sample 28 picked the bottled water. Was the bottled water selected significantly more often than would be expected by chance? Use a two tailed test with a significance of .05