Question

The mean annual incomes of certified welders are normally distributed with the mean of $75,000 and a population standard deviation of $3,500. The ship building association wishes to find out whether their welders earn more or less than $75,000 annually. The alternate hypothesis is that the mean is not $75,000. If the level of significance is 0.01, what is the critical value?

Answer 1

Solution:
Given in the question
the mean annual income of certified welders are normally distributed with
Mean = $75000
Standard deviation = $3500
The claim is that the mean is not $75000
So the null and alternate hypothesis can be written as follows:
Null hypothesis H0: = $ 75000
Alternate hypothesis Ha: $ 75000

this is the two-tailed test so, at alpha = 0.01, critical values from Z-table are as follows:
Z critical value for left tailed = -2.58
Z-Critical value for right-tailed = 2.58
The decision rule is if Ztest statistic value is less than -2.58 or greater than 2.58 than reject the null hypothesis else do not reject the null hypothesis.