Thread: determine the z-sgtatistic for two population samples

I'm having some trouble trying to figure out this question which deals with two population samples. The actual question is as follows:

On Assignment 2 we had n = 342, Σx = 6552 and Σx² = 127552. On Assignment 3 we had n = 311, Σx = 3667 and Σx² = 53389. Suppose I want to test H₀: μ₂-μ₃ = 0 against H_a: μ₂-μ₃ ≠ 0 at a significance level of α=0.05. What is the z-statistic and the conclusion.

I know the z statistic is:
z = [(x̄₁-x̄₂)-D₀] / sqrt([s₁²/n] + [s₂²/n])
where x̄ = Σx/n
and where s² = [Σx² - (Σx)²/n] / n-1
but I'm not exactly sure how I'm supposed to get the correct answer. The Solutions to this are as follows:

[quote]1.4588, -3.5045, do not reject H0 [/quote]

So, I plugged in plugged in the values and I get the following:
x̄₁ = 6552/342 = 19.158
x̄₂ = 3667/311 = 11.79099
D₀ = 0
s₁² = [127552 - (6552²/342)] / 341 = 5.9515
s₂² = [53389 - (3667²/311)] / 310 = 32.7465
So then if you plug in everything, you get:
z = [(19.158-11.79099)-0] / sqrt([5.9515/342] + [32.7465/311])
z = 21.029


and since the equation implies the rejection regions lie within the tail ends of the normal distribution, a/2 = 0.025 -> this means the non-rejection zone is μ ± 1.96


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this is where I get lost...

never mind, my prof said the answer key was incorrect. What i had was the correct answer.