I have come across a testing question that I do not know how to construct the hypothesis. The question is this: The GDP per capita of country Old-Men is a gaussian random variable with variance 10,000. The average GDP per capita has been found to be $30,000 until last year. It is claimed that this year, the GDP per capita has gone up by at least 20%. The variance remained the same. Construct a test to test this claim.
I have some trouble constructing the null hypothesis. I tried to use u=30,000 as the null hypothesis and u>30,000 as the test. But this way I cant test if it increased by at least 20%. If i use u=36,000 as the null hypothesis and u>36,000 as the test. I feel like this would always validate the claim as both null and test supports the claim. I am kinda lost here.
Thanks for any help.