I am having trouble with a question that asks: What sample size is needed if the probability of not detecting a change of one standard deviation is to be no more than 1%.
So the hypotheses is two sides, i.e H0:mu=mu0 and H1: mu is not equal to mu0. So H0 is rejected if |Xbar-mu|>c
I started by setting the Pr(|Xbar-mu|=1 standard deviation) ≤0.01 =beta (type 2 error)
So I am stuck here i know n must be discrete. I am unsure how to proceed, or whether the previous steps I took were correct.
I would appreciate any help. Thanks in advance.
Re: Hypotheses testing
I have a feeling you want to find the value of n so that three standard deviations (or standard errors) are in some particular interval.
For this you need to fix a standard error from your sample (or a standard deviation that is assumed for your population) and solve for n where se/SQRT(n) < 1/3 or 3*se/SQRT(n) < 1.
A value of 3 gives roughly 99.7% confidence which is what you are looking for as a rough sketch.