Question

2. (20 pts) At a large local hospital 20 teen volunteers worked a total of 172 hours with a sample standard deviation of 3.6. Thirty senior citizen volunteers worked a total of 366 hours with a sample standard deviation of 42, At a 01 level of significance can it be concluded that there is a difference in the two means? Use the P-value method. (You may assume the populations are normally distributed) : 4.2 .01 Claim (in words): The is difference nte two means Test value formula and inputs: 174 Test value

Answer 1

Sample #1   ---->   teens                  
mean of sample 1,    x̅1=   172.00                  
standard deviation of sample 1,   s1 =    3.60                  
size of sample 1,    n1=   20                  
                          
Sample #2   ---->   SENIOR                  
mean of sample 2,    x̅2=   366.00                  
standard deviation of sample 2,   s2 =    4.20                  
size of sample 2,    n2=   30                  
                          
difference in sample means =    x̅1-x̅2 =    172.0000   -   366.000   =   -194.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    3.97                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.1470                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -194.0000   -   0   ) /    1.1470   =   -169.14
                          
Degree of freedom, DF=   n1+n2-2 =    48                  
p-value =        0.0000 (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α =0.01, Reject null hypothesis                      
SO, IT is concluded that there is a difference in the two means at α=0.01