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(21.23) A study of the effect of exposure to color ( red or blue) on the ability

ID: 3157300 • Letter: #

Question

(21.23) A study of the effect of exposure to color ( red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects were asked to solve a series of puzzles while in a red-colored environment. The other half were asked to solve the same series of puzzles while in a blue-colored environment. The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.63 seconds with standard deviation 3.39; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.64.

The two-sample t statistic for comparing the population means has value (±0.001)

Explanation / Answer

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    two   tailed test.      
Calculating the means of each group,              
              
X1 =    9.63          
X2 =    15.84          
              
Calculating the standard deviations of each group,              
              
s1 =    3.39          
s2 =    8.64          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    21          
n2 = sample size of group 2 =    21          
Thus, df = n1 + n2 - 2 =    40          
Also, sD =    2.025335951          

where uD = hypothesized difference =    0
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -3.066157986   [ANSWER]

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Hi! You can also try the positive counterpart, t = 3.066157986, as the convention here is not given. Thanks!