Question

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital, and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is:

Answer 1

Ho :   µ =   30                  
Ha :   µ >   30       (Right tail test)          
                          
Level of Significance ,    α =    0.050                  
sample std dev ,    s =    20.0000                  
Sample Size ,   n =    16                  
Sample Mean,    x̅ =   40.0000                  
                          
degree of freedom=   DF=n-1=   15                  
                          
Standard Error , SE = s/√n =   20.0000   / √    16   =   5.0000      
t-test statistic= (x̅ - µ )/SE = (   40.000   -   30   ) /    5.0000   =   2.000
                          
critical t value, t* =        1.753   [Excel formula =t.inv(α/no. of tails,df) ]              
                          
p-Value   =   0.0320   [Excel formula =t.dist(t-stat,df) ]