Stuck trying to develop test statistic

Hi, I am stuck trying to develop a test stastic for Ho: 2*Mu1 = Mu2 vs. 2*Mu1 not=Mu2
assuming variances known

I think some modification has to be done to the test stastic Zo = (y_bar1 - y_bar2)/sqrt((var1/n1)+(var2/n2))
any help would be greatly appreciated, thanks


TS Contributor
What a lot of stats courses don't show you is that test statistics actually look like this (for example):

z = [(xbar1 - xbar2) - (mu1 - mu2)] / sqrt((var1/n1)+(var2/n2))

In most cases, mu1 - mu2 is hypothesized in the null case to be 0, so it "disappears." However, when you're presented with a situation where mu1-mu2 is not 0, it can be confusing.....