We have two random samples \({X_1}\), ..., \({X_{12}}\) and \({Y_1}\), ..., \({Y_{12}}\) from two populations. We want to show that the mean of Ys are greater than the mean of Xs.
What are the null hypothesis and the alternative hypothesis?
\(H_0: \mu_X=\mu_Y\) versus \(H_A: \mu\neq 160\)
\(H_0: \mu_X=\mu_Y\) versus \(H_A: \mu_X=\mu_Y\)
\(H_0: \mu_X<\mu_Y\) versus \(H_A: \mu_X=\mu_Y\)
\(H_0: \mu_X=\mu_Y\) versus \(H_A: \mu_X>\mu_Y\)
\(H_0: \mu_X=\mu_Y\) versus \(H_A: \mu_X<\mu_Y\)
Recall that we set the alternative hypothesis \(H_A\) as what we want to prove.
The correct setup is \(H_0: \mu_X=\mu_Y\) versus \(H_A: \mu_X<\mu_Y\).
The claim that we wish to prove \((\mu_X<\mu_Y)\) is always the alternative hypothesis.