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(Z-test)
Used
to compare two proportions created by two random samples or two subgroups of one random
sample.
Problem:
A survey was conducted of students from the Princeton public school system to determine if
the incidence of hungry children was consistent in two schools located in lower-income
areas. A random sample of 80 elementary students from school A found that 23% did not have
breakfast before coming to school. A random sample of 180 elementary students from school
B found that 7% did not have breakfast before coming to school.
Assumptions
Independent
random sampling
Nominal
level data
Large
sample size
State
the Hypothesis
Ho:
There is no statistically significant difference between the proportion of students in
school A not eating breakfast and the proportion of students in school B not eating
breakfast. 
Ha:
There is a statistically significant difference between the proportion of students in
school A not eating breakfast and the proportion of students in school B not eating
breakfast. 
Set
the Rejection Criteria
Use
z-distribution
table to estimate critical value
Alpha.05,
Zcv = 1.96
Compute
the Test Statistic
Estimate
of Standard Error
 where  and 
 
  
Test
Statistic
  
Decide
Results of the Null Hypothesis
Since
the test statistic 3.721 exceeds the critical value of 1.96, you conclude there is a
statistically significant difference between the proportion of students in school A not
eating breakfast and the proportion of students in school B not eating breakfast.
Software Output Example
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