Z- TEST
BETWEEN TWO
INDEPENDENT
PROPORTIONS
CHARL JAMES G. CRUIZ
IVY GRACE T. CORONEL
MARIA FE S. DAPAT
Definitions:
In statistics, a two-sample z-test for proportions is a
method used to determine whether two samples are
drawn from the same population.
The purpose of the z-test for independent proportions is
to compare two independent proportions.
While performing the test, Z-statistics is computed from
two independent samples and the null hypothesis is that
the two proportions are equal. In other words, the two
samples are coming from the same population.
In order to use two proportions Z-test, the two
populations must be normal or approximately normal and
two samples must be independent and randomly sampled
from the two populations.
• When conducting a z-test, the null and
alternative hypotheses, alpha and zscore should be stated. Next, the test
statistic should be calculated, and the
results and conclusion stated. A z-statistic,
or z-score, is a number representing how
many standard deviations above or below
the mean population a score derived from
a z-test is.
1
2
3
The two populations must be
normal or approximately normal
The two samples must be
randomly sampled from the two
populations
The two proportions must be
independent
Conditions:
P1 -hat is the proportion of the 1st sample
P2 -hat is the proportion of the 2nd
sample
n1 -is number of data samples in the 1st
sample
n2 - is number of data samples in the 2nd
sample
p-hat is mean of both the samples
Step 1: Create an Hypothesis
Ho
there is no significant
difference in the proportion
of male and female who
drop their subject
Ha
there is a significant
difference in the proportion
of male and female who
drop their subject
Step 2: Find the Critical value
a= 0.05
Tailed: TWO TAILED
Critical Value: -+1.960
Step 3: Solving
n1= 400
n2= 260
p1=30/400= 0.075
P2= 20/250= 0.08
p= 50/650= 0.076
0.075 - 0.08
Z=
-0.005
1
1
+ )
400
260
√ 0.076 (1- 0.076) (
-0.005
Z= 0.070224) (0.0025+0.00384615385
√
Z=
√ 0.070224) (0.00634615385)
-0.005
Z=
√ 0.00044554427
-0.005
Z=
0.0211079196
Z= -0.23
Step 4: Graphing, Decision, Conclusion
-0.23
-1.96
+1.96
Ho
Decision:
there is no significant difference in the proportion
of male and female who drop their subject
Accept Ho and Reject Ha
Ha
there is a significant difference in the proportion of
male and female who drop their subject
Step 1: Create an Hypothesis
Ho
there is no significant difference
between the proportion of Mrs.
Hanz and Mrs. Ramirez students
who passed the exam
Ha
there is no significant difference
between the proportion of Mrs.
Hanz and Mrs. Ramirez students
who passed the exam
Step 2: Find the Critical value
0.01
Z=
a= 0.05
Tailed: TWO TAILED
Critical Value: -+1.960
Z=
n1= 168
Step 3: Solving
n2= 297
√ 0.583 (0.417) (0.00595238095 +0.00336700337)
0.01
Z=
P2= 172/297= 0.579
Z=
0.589 - 0.579
Z=
1
1
√ 0.583 (1- 0.583) (168 + 297)
1
0.01
p1=99/168= 0.589
p= 271/465= 0.583
1
√ 0.583 ( 0.417) (168 + 297)
Z=
√
(0.243111) (0.00931938432)
0.01
√ 0.00226564484
0.01
0.047598790932
Z=0.21
Step 4: Graphing, Decision, Conclusion
0.21
-1.96
+1.96
Ho
Decision:
there is no significant difference between the
proportion of Mrs. Hanz and Mrs. Ramirez students who
passed the exam
Accept Ho and Reject Ha
Ha
there is no significant difference between the
proportion of Mrs. Hanz and Mrs. Ramirez students who
passed the exam
You are testing 2 flu drugs A and B. Drug A
works on 41 people out of a sample of 195. Drug B
works on 351people in sample of 605. Are the two
Drugs comparable? Use a 5% alpha level.
Formula:
References
https://influentialpoints.com/Training/z-test_for_independent_proportions-principlespropertiesassumptions.htm#:~:text=The%20purpose%20of%20the%20z,to%20as%20the%20risk%2
0difference.
https://www.spss-tutorials.com/z-test-2-independent-proportions/
https://vitalflux.com/two-sample-z-test-for-proportions-formula-examples/