Chapter 9.3, Problem 95E

i.

To determine

To explain: is it proper to conclude that for four people have ESP.

Answer to Problem 95E

It is possible that $4$ of the $500$ subjects has a $P-$ value below the $0.01$ .

Explanation of Solution

Given:

  $\begin{array}{l}n=500\\ x=4\\ P<0.01\end{array}$

Calculation:

No, because one would expect about $1\%$ of the $500$ subjects to have $P-$ value of $0.01$ . As $1\%$ of the $500$ subjects corresponds with $5$ subjects, so it is possible that $4$ of the $500$ subjects has a $P-$ value below the $0.01$ .

The $P-$ value is actually the possibility o getting test results or more extreme when null hypotheses of random guessing is true. So it is likely that these $4$ subjects with a $P-$ value below $0.01$ had no EPSP.

Conclusion:

Thus, it is possible that $4$ of the $500$ subjects has a $P-$ value below the $0.01$ .

ii.

To determine

To explain: Researchers now do to test whether any of these four subjects has ESP.

Answer to Problem 95E

Researchers should retest these $4$ subjects for ESP

Explanation of Solution

Given:

  $\begin{array}{l}n=500\\ x=4\\ P<0.01\end{array}$

Calculation:

Researchers should retest these $4$ subjects for ESP. if they again perform significantly better than random guessing, then they most likely have ESP.

Conclusion:

Thus, Researchers should retest these $4$ subjects for ESP