Question

In a maze running study, a rat is run in a T maze and the result of each run recorded. A reward in the form of food is always placed at the right exit. If learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place, the rat should randomly choose either exit. Suppose that the rat is given n = 100 runs in the maze and that he chooses the right exit x = 62 times. Would you conclude that learning is taking place? (Use α = 0.01.)

Answer 1

There is significant learning

Explanation:

This is a test on comparison of a single proportion with a hypothesized proportion.

The subject of interest is whether rats really learn.

`H_0: p = 0.5\\H_a: p >0.5\\`

(Right tailed test)

n =100

Sample proportion p = 0.62

Std error of p assuming H0 to be true is

=
`\sqrt{(pq)/(n) } =0.05`

p difference = 0.12

Z statistic = p difference/std error =
`(0.12)/(0.05) \\=2.4`

p value = 0.0082

Since p <0.01, our alpha we reject null hypothesis

There is significant learning