(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!
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