Jamal suspects that his diastolic blood pressure is higher w

Jamal suspects that his diastolic blood pressure is higher when he is at work than his diastolic blood pressure when he is not at work. He is going to test this statement based on blood pressure readings at randomly selected times in the above two situations.

Here are the data (units in mmHg)

at work

84 84 86   86   87   87   87   88   90   97   99

   not at work

    77   78   79   79   80   83   84   85   85   89

Solution

As it is not given, let alpha = 0.05.

Let u1 = mean of at work
u2 = mean of not at work

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  

At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    88.63636364          
X2 =    81.9          
              
Calculating the standard deviations of each group,              
              
s1 =    4.945153734          
s2 =    3.871548642          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    19          
Also, sD =    1.929256174          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    3.491689558          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +   1.729132812      
              
Also, using p values,              
              
p =    0.001220472          
              

Thus, as P < 0.05, we reject Ho.

Thus, there is significant evidence that his diastolic blood pressure is higher when he is at work than his diastolic blood pressure when he is not at work. [CONCLUSION]