Construct the 95% confidence interval for the difference between the population means

Question

Xbar 1 = 31.0

Stand Dev =94.3

N1 = 29

Xbar 2 =26

Stand Dev 2 =90.8

N2 =29

I do not understand the formula.

I am looking for step by step with calculations,

For an example the first part of the formula is (xbar 1-xbar2) so that would be 5, but I do not know how to get the +/- Z∝/2 .

The second part of the formula is the square root of (stand deviation 1 /n1 + stand deviation 2/n2)

So I have that calculated as 2.5264

So I have it as 5 +/- {I do not know how to get Z∝/2 2.5264.

How do i get the Z∝/2?

Answer 1

Hello. You can find the Za/2 by taking 1 - a/2

1 - (.05/2) = 0.975

You can go to excel and type in = NORM.S.INV(probability) to get the appropriate critical value for Z.

As for the question, are those standard deviations population standard deviations or sample standard deviations? That would make the difference between Z-test and a T-test. Judging by the sample sizes, I would encourage you to use the formula for obtaining a confidence interval for T. You would find the critical value there by going to a t-table chart and using df for both groups (n1 + n2 -2) , the alpha level , and the tail information and finding the critical value from there. I hope this helps.

Let me know if you have any additional questions.