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Table of Contents

 


 

Comparing Proportions From Two Independent Samples

(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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