Several students were tested for reaction times (in thousandths of a second) usi

Question

Several students were tested for reaction times (in thousandths of a second) using their right and left hands. (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the subject.) Results from five of the students are included in the graph to the right. Use a 0.10 significance level to test the claim that there is no difference between the reaction times of the right and left hands. Click the icon to view the reaction time data table. Right Hand What are the hypotheses for this test? Let mu_d be the of the right and left hand reaction times. H0:mu_d 0 H_1: mu_d 0 What is the test statistic? t = (Round to three decimal places as needed.) Identify the critical value(s). Select the correct choice below arid fill the answer box within your choice. (Round to three decimal places as needed.) The critical value is t = The critical values are t = plusminus What is the conclusion? There enough evidencee to warrant rejecti

Explanation / Answer

1. Mean of differences [as this is a paired t test]
2. Ho:   ud   =   0  
3. Ha:   ud   =/   0   [ANSWERS]

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Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/   0  
At level of significance =    0.1          
As we can see, this is a    two   tailed test.  
The differences are

12
15
26
13
21
  
              
Calculating the standard deviation of the differences (third column):              
              
s =    9.649540733          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    4.315405806          
              
Calculating the mean of the differences (third column):              
              
XD =    17.4          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.032065762   [ANSWER, TEST STATISTIC]      
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As df = n - 1 =    4          
              
Then the critical value of t is              
              
tcrit =    +/-   2.132   [OPTION B, CRITICAL VALUES]  
  
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As |t| > 2.132, we reject Ho.

4. IS
5. A DIFFERENCE [ANSWER]

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