Question

We are interested in studying whether there is a difference in the time it takes for patients to recover after surgery for two given hospitals. A simple random sample of cardiac surgery patients were taken from each hospital. The results were summarized in the table below. It shows the hospital one attended (Hospital A vs Hospital B), and the average length of stay (measured in days) for patients after cardiac surgery.

	n	Average Length of Stay (in days)	Sample Standard Deviation, s
Hospital A	30	16	4
Hospital B	35	12	3
Combined (Hospital A + B)	65	14	3.7

Test whether there is a significant difference in the length of stay for patients depending on which hospital they attended for surgery. Assume alpha = 0.05.

1. State the null and alternative hypothesis

2. Set alpha

3. Compute the Test Statistic

4. Determine p-value

5. Conclude (Select either: Reject the Null OR Fail to Reject the Null)

Answer 1

1)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0

2)

α=0.05

3)

Sample #1   ---->   1                  
mean of sample 1,    x̅1=   16.00                  
standard deviation of sample 1,   s1 =    4.00                  
size of sample 1,    n1=   30                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   12.00                  
standard deviation of sample 2,   s2 =    3.00                  
size of sample 2,    n2=   35                  
                          
difference in sample means =    x̅1-x̅2 =    16.0000   -   12.0   =   4.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    3.4960                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.8698                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   4.0000   -   0   ) /    0.87   =   4.5986

4)

Degree of freedom, DF=   n1+n2-2 =    63

p-value =        0.0000

5)

Conclusion:     p-value <α , Reject null hypothesis