Suppose we are interested in performing a hypothesis test on the population standard deviation of the run time for a bit of optimization code that I have attempted to improve. The initial code that I was adapting had a standard deviation of 3 minutes. I believe that the newest iteration has a standard deviation that is actually less than 3 minutes. What would be the null hypothesis for this test

Null hypothesis:

Alternative hypothesis:

And we can test this hypothesis with a chi square test for the population deviation of interest.

Step-by-step explanation:

For this case what we are trying to proof is if the true population standard deviation is less than 3 minutes and that needs to represent the alternative hypothesis.

Then by the complement rule we need to have the null hypothesis. Based on this the correct system of hypothesis are:

Null hypothesis:

Alternative hypothesis:

And we can test this hypothesis with a chi square test for the population deviation of interest.

you just switch the numbers basically so it would be 3/17