Question

QSR magazine assessed the work of McDonalds and Taco Time restaurants in terms of their service time in seconds. For the sample of 308 observations from Taco Time restaurants, the mean service time was 158.03 seconds with a standard deviation of 33.8 seconds. For the sample of 317 observations from McDonalds restaurants, the mean service time was 189.49 seconds with a standard deviation of 41.3 seconds. Is there a difference in the mean service times between Taco Time and McDonald's restaurants?

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   158.030                  
standard deviation of sample 1,   s1 =    33.8000                  
size of sample 1,    n1=   308                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   189.490                  
standard deviation of sample 2,   s2 =    41.3000                  
size of sample 2,    n2=   317                  
                          
difference in sample means =    x̅1-x̅2 =    158.0300   -   189.5   =   -31.46  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    37.7907                  
std error , SE =    Sp*√(1/n1+1/n2) =    3.0236                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -31.4600   -   0   ) /    3.02   =   -10.4049
                          
Degree of freedom, DF=   n1+n2-2 =    623                  
t-critical value , t* =        1.964   (excel formula =t.inv(α/2,df)              
Decision:   | t-stat | > | critical value |, so, Reject Ho                      
p-value =        0.0000   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      
                          
There is enough evidence of significant difference