Contents
Statistics
"Difference between Two Sample Proportions"
What are sample proportions?
What is a two sample ztest of two proportions all about?
what are the steps in testing the difference between two sample proportions?
The sample proportion
is the proportion of individuals in a sample sharing a certain trait,
denoted p
In this section, you will learn how to use a ztest to test the difference between two population proportions p and p using a sample proportion from each population.
When is a two sample ztest of two proportions used?
What are the symbols used?
To use a ztest to test such a difference, the following conditions are necessary:
1. The samples must be independent.
2. The samples must be large enough to use a normal sampling distribution. That is:
n p ≥> 5, n q ≥> 5, n p ≥> 5, n q >≥ 5
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The comparison of two sample
proportion or percentages to
determine if there is a significant
difference is similar to the
analysis of the arithmetic means
of two samples.
If the null hypothesis states that p1 = p2, then the expression, p1  p2 is equal to 0 in the preceding test.
examples and exercises
Prepared By:
Baguindo, Rechille Mae C.
Ortiz, Necergio D.
Pamintuan, Jolicia Aicila Marie R.
Domingo, Joe Angiolo D.
Apostol, Mark Joseph G.
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You want to determine whether there is a difference in the proportions. So, the null and alternative hypotheses are:
Ho: p1 ≥ p2 and
Ha: p1 < p2 (claim)
Because the test is lefttailed and the level of significance is = 0.01, the critical value is
2.33. The rejection region is z < 2.33
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Problem 1: TwoTailed Test
Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a a simple random sample of 100 women and 200 men from a population of 100,000 volunteers.
At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance.
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