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With
Homogeneity of Variance 
Used
to compare two sample means. The independent
variable is nominal level data and the dependent variable is interval/ratio level.
Problem:
You have obtained the number of years of education from one random sample of 38 police
officers from City A and the number of years of education from a second random sample of
30 police officers from City B. The average years of education for the sample from City A
is 15 years with a standard deviation of 2 years. The average years of education for the
sample from City B is 14 years with a standard deviation of 2.5 years. Is there a
statistically significant difference between the education levels of police officers in
City A and City B?
Assumptions
Random
sampling
Independent
samples
Interval/ratio
level data
Organize
data
City
A (labeled sample 1)
City
B (labeled sample 2)
State
Hypotheses
Ho:
There is no statistically significant difference between the mean education level of
police officers working in City A and the mean education level of police officers working
in City B. 
For
a 2-tailed hypothesis test
Ha:
There is a statistically significant difference between the mean education level of police
officers working in City A and the mean education level of police officers working in City
B. 
For
a 1-tailed hypothesis test
Ha:
The mean education level of police officers working in City A is significantly greater
than the mean education level of police officers working in City B.
Set
the Rejection Criteria
Determine
the degrees of freedom (df) = (n1+n2)-2
df
= 38+30-2=66
Determine
level of confidence -- alpha
(1 or 2-tailed test)
Use
the t-distribution
table to determine the critical value
If
using 2-tailed test
Alpha.05,
tcv= 1.997
If
using 1-tailed test
Alpha.05,
tcv= 1.668
Compute
Test Statistic
Standard
error
Test
Statistic
 
Decide
Results
If
using 2-tailed test
There
is no statistically significant difference between the mean years of education for police
officers in City A and mean years of education for police officers in City B. (note: the
test statistic 1.835 does not meet or exceed the critical value of 1.997 for a 2-tailed
test.)
If
using 1-tailed test
Police
officers in City A have significantly more years of education than police officers in City
B. (note: the test statistic 1.835 does exceed the critical value of 1.668 for a 1-tailed
test.)
Software Output Example
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