Question

Donna wants to test whether or not drinking coffee will immediately increase heart rate while sitting in class. Six people measured their heart rates before drinking coffee and then the same six people took their heart rates after drinking their coffee. Please calculate the t-statistic for this experiment; then state the critical value; then come to a conclusion concerning the null hypothesis; and then state what the implications are concerning drinking coffee.

No Coffee                   Coffee

79                                  84

71                                  78

84                                  87

66                                  75

74                                  80

76                                  82

Answer 1

Ho :   µd=   0
Ha :   µd <   0

mean of difference ,    D̅ =ΣDi / n =   -6.0000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.0000                  
                          
std error , SE = Sd / √n =    2.0000   / √   6   =   0.8165      
                          
t-statistic = (D̅ - µd)/SE = (   -6   -   0   ) /    0.8165   =   -7.348
                          
Degree of freedom, DF=   n - 1 =    5                  
t-critical value , t* =        -2.0150 [excel function: =t.inv(α,df) ]              
                          

Decision: test stat < critical value , Reject null hypothesis                     

there is enough evidence to conlcude that drinking coffee will immediately increase heart rate