Need help finding standardized test statistics!!!! PLEASE!!

#1
I have two homework problems that I can't seem to find the formulas on how to do this anywhere! Can anyone help me? I've tried to follow what I thought were the formulas but are coming up with answers that are not options. I'm not sure if I should put what the answer options are on here or not....

1st question: Find the standardized test statistic, t, to test the claim that u1=u2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that o 2 (over)1 not equal to o 2 over 2.
N1= 25, N2= 30, X1=27, X2= 25, S1= 1.5, S2= 1.9

2nd question: Find the standardized test statistic, z to test the claim that p1=p2. The sample statistics listed below are from independent samples.
n1=50, x1=35, n2=60, x2= 40

If anyone can help me I would really appreciate it
 

Dragan

Super Moderator
#2
1st question: Find the standardized test statistic, t, to test the claim that u1=u2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that o 2 (over)1 not equal to o 2 over 2.
N1= 25, N2= 30, X1=27, X2= 25, S1= 1.5, S2= 1.9


If anyone can help me I would really appreciate it

Well, can you help me? That is, what does: "Assume that o 2 (over)1 not equal to o 2 over 2." imply?


Next, does u1=u2 imply that the two population means are equal?

In view of the above, I'm going to assume that the question is associated with a two-independent samples t-test.

Thus,

t = (XBar1 - XBar2) / Sqrt [ ( Sp^2 * ( 1/N1 + 1/N2 )]

where,

Sp^2 is the pooled variance and equal to

Sp^2 = ( (N1 - 1) * Var1 + (N2 - 1) * Var2 ) / (N1 + N2 - 2)

and where Var1 and Var2 are the variances associated with groups 1 and 2 where are equal to std1^2 and std2^2 (the standard deviations of the two groups)

I'll stop at this point.