Question

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $8,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The data collected from 36 certified welders indicate that the sample mean annual income is $47,500. If the level of significance is 0.10.
What are the null and alternative hypothesis to test that the mean is not $50,000?

		H0: µ ≤ $50,000; Ha: µ > $50,000
		H0: µ $47,500; Ha: µ ≠ $47,500
		H0: µ $50,000; Ha: µ ≠ $50,000
		H0: µ ≥ $50,000; Ha: µ < $50,000

Answer 1

The null hypothesis is a statement or position such that there is no relationship or associations between two items. And the alternative hypothesis is a statement which indicates that there is some statistically significant relationship between two variables. So we choose that situation where there is no change from the past or existing situation as null hypothesis and it there is any change then that would be considered as alternative hypothesis.  

Here the ship building associations wants to find whether the welders earn is more or less than the average earn 50000. So the null hypothesis is the earn is equals to mean earn 50000. And the alternative hypothesis is that the mean earn is not equals to 50000.

In mathematical term

H0: =$50000 ag Ha : $50000