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Table of Contents

 


 

Comparing Two Independent Sample Means (T-test)

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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