Q.6 - The Practice of Statistics for AP

Question

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over $1000$ Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by 

(a) using only volunteers from the basketball team in the experiment. 

(b) using $A=0.01$ instead of $A=0.05$. 

(c) using $A=0.05$ instead of $A=0.01$. 

(d) giving the drug to $25$ randomly selected students instead of $50$. 

(e) using a two-sided test instead of a one-sided test. 

Step-by-Step Solution

Answer

The power of the test to detect an average increase in height of one inch could be increased by   (C) Using $\alpha =0.05$ instead of $\alpha =0.01$.

Step 1: Given Information

Over $1000$ Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug 

Step 2: Explanation

Increasing the sample size will boost the power (Because we will be able to create better estimates if we have more information on the population.).

Increase the level of relevance (because this increases the probability of making a Type I error while decreasing the probability of making a Type II error; because the power is $1$, the probability of making a Type II error is reduced, and therefore the power is increased).

Making the alternative proportion $p$ or mean $\mu$ more extreme.

The correct answer is then (c) Using $\alpha =0.05$ instead of $\alpha =0.01$.