To test the effect of alcohol in increasing the reaction tim

To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 3 ounces of 40% alcohol, the reaction time for each of the seven people was measured again. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use = 0.05. (Use before after = d. Round your answers to three decimal places.)

Test statistic:  t = ?

Rejection region:  If the test is one-tailed, enter NONE for the unused region.

t > ?

t < ?

Solution

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    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    1.505042031          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.568852418          
              
Calculating the mean of the differences (third column):              
              
XD =    -1          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -1.757925198   [ANSWER, TEST STATISTIC]      
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As df = n - 1 =    6          
              
Then the critical value of t is              
              
tcrit =    -2.446911851      

Hence,

Reject Ho when t < -2.4469. [ANSWER]

t > NONE. [ANSWER]