Question

12) The president is concerned about the escalating costs of providing health care in the United States. One of the components contributing to the increasing cost is the length of the hospital stay of a patient. In a sample involving 28 patients the mean time was ? = 4.6 days with standard deviation ? = 1.3 days. Do these results demonstrate that the true mean stay of a patient is significantly longer than 4 days? Carry out a test using a 2.5 percent level of significance. Assume a normal distribution.

Answer 1

Ho :   µ =   4                  
Ha :   µ >   4       (Right tail test)          
                          
Level of Significance ,    α =    0.025                  
sample std dev ,    s =    1.3000                  
Sample Size ,   n =    28                  
Sample Mean,    x̅ =   4.6000                  
                          
degree of freedom=   DF=n-1=   27                  
                          
Standard Error , SE = s/√n =   1.3000   / √    28   =   0.2457      
t-test statistic= (x̅ - µ )/SE = (   4.600   -   4   ) /    0.2457   =   2.442
                          
  
p-Value   =   0.0107   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α=0.025, Reject null hypothesis                       
Conclusion: There is enough evidence to conclude that the true mean stay of a patient is significantly longer than 4 days