Consumption of large amounts of alcohol is known to increase

Consumption of large amounts of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after the consumption of 2 ounces of alcohol. Do the data below suggest that consumption of 2 ounces of alcohol increases mean reaction time?

Identify the null hypothesis and the alternative hypothesis.

Solution

Let ud = u(x(after) - x(before))              

Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0  

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At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    0.887625365          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.396958131          
              
Calculating the mean of the differences (third column):              
              
XD =    0.8          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.015325895          
              
As df = n - 1 =    4          
              
Then the critical value of t is              
              
tcrit =    +   2.776445105      
              
Thus, as t < 2.776, we   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
There is no significant evidence at 0.05 level that consumption of 2 ounces of alcohol increases mean reaction time. [CONCLUSION]