Testing:
$H O: u \geq 13.9$
$H 1: u< 13.9$
At $a=0.02$ the rejection region is
\(\boxed{\text{The rejection region is } z < -2.05}\)
Step 1 :We are given a null hypothesis \(H O: u \geq 13.9\) and an alternative hypothesis \(H 1: u<13.9\). The significance level is \(a=0.02\).
Step 2 :We are asked to find the rejection region for a one-tailed hypothesis test. This is a left-tailed test because we are testing for a value that is less than a certain number.
Step 3 :The rejection region would be any z-score that corresponds to a probability less than the significance level.
Step 4 :To find the z-score that corresponds to a probability of 0.02, we can use the standard normal distribution table.
Step 5 :The z-score that corresponds to a significance level of 0.02 is approximately -2.05. This means that any z-score less than -2.05 would fall in the rejection region.
Step 6 :\(\boxed{\text{The rejection region is } z < -2.05}\)