Question

ch 23* in an experiment to learn if substance m can help restore memory, the brains of 20 rats were treated to damage their memories. the rats were trained to run a maze. after a day, 10 rats were given m, and seven of them succeeded in the maze; only two of the 10 control rats were successful. the z test for this scenario
may be inaccurate because some counts of successes and failures are too small.
may be inaccurate because the populations are too small.
is reasonably accurate because the conditions for inference are met.

Explanation:

For a z - test for two - proportion, the conditions are \(n_1p_1\geq5\), \(n_1(1 - p_1)\geq5\), \(n_2p_2\geq5\), \(n_2(1 - p_2)\geq5\). In the control group, \(n_2 = 10\) and \(p_2=\frac{2}{10}=0.2\). Then \(n_2(1 - p_2)=10\times(1 - 0.2)=8\) and \(n_2p_2 = 10\times0.2 = 2\lt5\). The counts of successes (\(n_2p_2 = 2\)) in the control group is too small.

Answer:

may be inaccurate because some counts of successes and failures are too small.