Suppose you are considering two normal populations with unknown means μ1 and μ2 respectively. Variances are known to be σ1 and σ2 respectively. Show how you would test the following hypothesis against the two-sided alternatives H0 : μ−μ=0

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- September 5th 2012, 08:13 AMhomalinaTesting Hypothesis - How do we do this?
Suppose you are considering two normal populations with unknown means μ1 and μ2 respectively. Variances are known to be σ1 and σ2 respectively. Show how you would test the following hypothesis against the two-sided alternatives H0 : μ−μ=0

- September 12th 2012, 12:12 AMchiroRe: Testing Hypothesis - How do we do this?
Hey homalina.

Hint: what is the distribution of (X_bar - Y_bar) - (mu1 - mu2) going to be? You already know the variances and that they come from a normal distribution, and any linear combination of normal distributions gives back a normal.

With this information, what is the distribution of (X_bar - Y_Bar) and how do you standardize it? (Another hint: you assume mu1 - mu2 = 0).