Question

A major agricultural company is testing a newvariety of wheat to determine whether it is more resistant tocertain insects than is the current wheat variety. The pro-portion of a current wheat crop lost to insects is $4\%$. Thus,the company wishes to test the following hypotheses:

$H_{0:p}=0.04$

$H_{0:p}<0.04$

Which of the following significance levels and sample sizes

would lead to the highest power for this test?

$\text{(a)}n=200\text{and}\alpha =0.01$

$\text{(b)}n=400\text{and}\alpha =0.05$

$\text{(c)}n=400\text{and}\alpha =0.01$

$\text{(d)}n=500\text{and}\alpha =0.01$

$\text{(e)}n=500\text{and}\alpha =0.05$

Short answer

$\text{e)}n=500,\alpha =0.05$

Step-by-step solution

Given information

we have been given five options from which one is correct and the correct is (e)

Simplify

While it is possible to derive the power of a given function

$n=500\text{and}\alpha =0.05$

$\text{The higher the sample size, the more power to detect differences.}$