A study of visual and auditory reaction time is conducted fo

A study of visual and auditory reaction time is conducted for a group of college basketball players. Visual reaction time is measured by the time needed to re-spond to a light signal, and auditory reaction time is measured by the time needed to respond to the sound of an electric switch. Fifteen subjects were measured with time recorded to the nearest millisecond:

Solution

We let alpha = 0.05, as it is not given.

Let ud = u(visual) - u(auditory)

Formulating the null and alternative hypotheses,              
              
Ho:   ud   >=   0  
Ha:   ud   <   0  
At level of significance =    0.05          
As we can see, this is a    left   tailed test.      
              
Calculating the standard deviation of the differences
              
s =    33.70346881          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    8.702198226          
              
Calculating the mean of the differences
              
XD =    16.93333333          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    1.945868491          
              
As df = n - 1 =    14          
              
Then the critical value of t is              
              
tcrit =    -   2.144786688      
              
As |t| < 2.1448,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the visual reaction times is slower than the auditory reaction time at 0.05 level.