Question 760434: Given a sample of n1 = 40 from a population with known standard deviation σ1 =20, and an independent sample of n2 = 50 from another population with known standard deviation σ2 = 10, what is the value of the Z-test statistic for testing H0: μ1 = μ2 (μ1 – μ2 = 0) if x-bar1 = 72 and x-bar2 = 66.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the following definitions apply to this problem:
m1 = mean of sample 1
s1 = standard deviation of population 1
n1 = sample size of sample 1
m2 = mean of sample 2
s2 = standard deviation of population 2
n2 = sample size of sample 2
z = z-score of the difference between the mean of sample 1 and sample 2.
the standard error for this two sample z-test would be calculated as shown below as far as i know based on references from the web.
one such reference can be found at http://www.stat.ucla.edu/~cochran/stat10/winter/lectures/lect21.html
se = sqrt(s1^2/n1 + s2^2/n2)
you find s1^2/n1 and you find s2^2/n2 and you add them together and you then take the square root and you have the standard error for the test.
your numbers are:
m1 = 72, n1 = 40 s1 = 20
m2 = 66, n2 = 50, s2 = 10
from this information, you calculate se as follows:
se = sqrt(20^2/40 + 10^2/50) = 3.4641
to find the z-score, you calculate m1 - m2 and then divide it by 3.4641 and you get:
z = (m1-m2) / se = (72-66) / 3.4641 = 6 / 3.4641 = 1.7321
note:
s1^2 means the variable with the name of s1 squared.
likewise with s2
m1-m2 means the variable with the name of m2 subtracted from the variable with the name of m1.
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