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Small sample test of a difference between two means
Sociologists have been particularly interested in the success of Asian Americans despite
racial discrimination in the U.S. A sociologist took a random sample of27 Japanese
American men and found their mean annual earnings to be $22,907 with a standard
deviation of$11,120. She also took a random sample of32 Non-Hispanic white men and
found their mean annual earnings to be $24,891 with a standard deviation of$14,225.
You may assume earnings are normally distributed. Is there a significant difference in
annual earnings between Japanese American men and white men? Set a = .05
Japanese White
X
J
=22,907 Xw =24,891
sJ=11,120 sw=14.225
N
J
=27 N
w
=32
We assume: independent samples, random samples, level of measurement is interval
ratio, equal population variances (you are allowed to assume this unless stated otherwise),
the sampling distribution is normal
Ho: /lJ-/lw=O
HI: /lJ-/lwF
O
o~s
'.
Sampling Distribution = t di...

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