Question

Suppose the null and alternative hypothesis for a significance test are defined as

H0: μ=$40$$\frac{305}{1526}$$=0.200=20.0\%$H0 : μ=$40$

Ha: μ<$40$$\frac{305}{1526}=0.200=20.0\%$Ha : μ<$40$

Which of the following specific values for Ha will give the highest power? a. μ=$38$$\frac{305}{1526}=0.200=20.0\%$$\mu =38$

b. μ=$39$$\frac{305}{1526}=0.200=20.0\%\mu =39$

c. μ=$41$$\frac{305}{1526}=0.200=20.0\%\mu =41$

d. μ=$42$$\frac{305}{1526}=0.200=20.0\%\mu =42$

e. μ=$43$ $\frac{305}{1526}=0.200=20.0\%\mu =43$

Short answer

The correct option is - (a)$\mu =38$will give the highest power .

Step-by-step solution

Given Information 

We are given a null hypothesis and alternate hypothesis for a given significance test . We need to find which will give the highest power .

Explanation

The null and alternate hypothesis give the highest power when it is less than and furthest from $40$. So, the given furthest value is $38$. Hence it will give the highest power .