Question

In an experiment to learn whether substance M can help restore memory, the brains of $20$rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, $10$rats (determined at random) were given substance M and $7$of them succeeded in the maze. Only $2$of the $10$control rats were successful. The two-sample z test for the difference in the true proportions

a. gives $z=2.25,P<0.02$ .

b. gives $z=2.60,P<0.005$ .

c. gives $z=2.25,P<0.04$ but not$<0.02$

d. should not be used because the Random condition is violated.

e. should not be used because the Large Counts condition is violated.

Short answer

Option (e) is correct.

Step-by-step solution

Given Information

It is given that Normal requirement requires that the number of failures in the number of successes in both samples are greater than $10$ .

Explanation

In first sample, there are $7$successes and $2$successes in second sample. Normal condition is not satisfied.

It should not be used as normal condition is violated.

Option (e) is correct.