Difference Between Means

Hypothesis Testing of the Difference Between Two Means
Do employees perform better at work with music playing.  The music was turned on during the working hours of a business with 45 employees.  There productivity level averaged 5.2 with a standard deviation of 2.4.  On a different day the music was turned off and there were 40 workers.  The workers' productivity level averaged 4.8 with a standard deviation of 1.2.  What can we conclude at the .05 level?
Solution
We first develop the hypotheses
        H₀:  m₁ - m₂  =  0       
        H₁:  m₁ - m₂  >  0
Next we need to find the standard deviation.  Recall from before, we had that the mean of the difference is 
        m_x  =  m₁ - m₂ 
and the standard deviation is 

 s_x  =      

We can substitute the sample means and sample standard deviations for a point estimate of the population means and standard deviations.  We have

        
and 
Now we can calculate the t-score.  We have
                    0.4
        t  =                       =  0.988
                   0.405
To calculate the degrees of freedom, we can take the smaller of the two numbers n₁ - 1 and n₂ - 1.  So in this example we use 39 degrees of freedom.  The t-table gives a value of 1.690 for the t_.95 value.  Notice that 0.988 is still smaller than 1.690 and the result is the same.  Since the t-score is smaller than 1.690, we fail to reject the null hypothesis and state that there is insufficient evidence to make a conclusion about employees performing better at work with music playing. 




POSTED BY: VON ERJUN SABUSAP