Community Health System recently acquired Mercy Hospital The

Community Health System recently acquired Mercy Hospital. The Director of Nursing is evaluating the difference in compensation for Registered Nurses between the Hospitals. Her concern is the Nurses at Mercy Hospital are unionized. Here is a table summarizing her findings. Would it be reasonable for her to conclude that the Union Nurses earn more on average? Group Mean Wage Population Standard Deviation Sample Size Union $41.50 $4.50 40 Non-Union $39.60 $3.80 45 Step 1. Step 2. The 0.05 level of significance was chosen Step 3. Step 4. Step 5.

Solution

Set Up Hypothesis
Null, Union Nurses earn equals to in average Ho: u1 < u2
Alternate, Union Nurses earn more on average 1: u1 > u2
Test Statistic
X(Mean)=41.5
Standard Deviation(s.d1)=4.5
Number(n1)=40
Y(Mean)=39.6
Standard Deviation(s.d2)=3.8
Number(n2)=45
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=41.5-39.6/Sqrt((20.25/40)+(14.44/45))
Zo =2.09
| Zo | =2.09
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo | =2.089 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 2.09 ) = 0.01835
Hence Value of P0.05 > 0.01835,Here we Reject Ho

Conclude that Union Nurses earn more on average