Chapter PV, Problem 34RE

(a)

To determine

To indicate whether the power of test will increase, decrease or remain the same, assuming all other aspects of the situation remain unchanged.

Answer to Problem 34RE

The power of test will increase.

Explanation of Solution

It is given that we are replicating the experiment. So, if we increase the number of subjects from $\text{40 to 100}$ . Then, we can say that as the sample size increases from $\text{40 to 100}$ , we have more information about the population and thus our estimates will be more accurate, which increases the power of test.

(b)

To determine

To indicate whether the power of test will increase, decrease or remain the same, assuming all other aspects of the situation remain unchanged.

Answer to Problem 34RE

The power of test decreases.

Explanation of Solution

It is given that we are replicating the experiment. So, if we require a higher standard of proof, changing from $\alpha =0.05\text{ to }\alpha =0.01$ , then we can say that as the significance level decreases, the probability of Type-I error decreases and thus the probability of a Type-II error increases. Since the power is one decreased by the probability of making a Type-II error so the power of test decreases.