Question

Section I: Multiple ChoiceChoose the best answer for Questions AP4.1–AP4.40.
AP4.1 A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than the current wheat variety. The proportion of a current wheat crop lost to insects is 0.04. Thus, the company wishes to test the following hypotheses:
$H_0:p=0.04$

$H_a:p<0.04$

Which of the following significance levels and sample sizes would lead to the highest power for this test?
a. $n=200$ and $\alpha =0.01$
b. $n=400$and $\alpha =0.05$
c.$n=400$and $\alpha =0.01$
d. $n=500$and $\alpha =0.01$
e. $n=500$ and $\alpha =0.05$

Short answer

The correct answer is option (e) $n=500$ and $\alpha =0.05$.

Step-by-step solution

Given information

To determine the significance levels and sample sizes that lead to the highest power for the test.

Explanation

A large agricultural corporation is evaluating a new wheat type to see if it is more bug resistant than the current wheat variety. While the power for a given value of the alternative can potentially be calculated.

Simple notions can be used to address the question:
The larger the sample size size, better possible it is to identify variations.
The lower the power, the more difficult it is to reject the null hypothesis, and the more likely you are to commit a type Il error.
As a result, when alpha and sample size are both large, the power is maximized.
As a result, option (e) is the proper answer.