Problem 3 (3 points). A study of the effect of exposure to color (red or blue) o
ID: 2949259 • Letter: P
Question
Problem 3 (3 points). 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 time taken to solve the puzzles was recorded for each subject. The subjects in the red-colored environment had a mean time for solving the puzzle of 9.64 seconds with standard deviation 3.43. The subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65 Conduct a two-sample t significance test to determine if these data provide significant evidence at the 1% level that people solve puzzles more quickly in a red environment than in a blue one.Explanation / Answer
Solution:-
3)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: uRed> uBlue
Alternative hypothesis: uRed < uBlue
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.03057
DF = 40
t = [ (x1 - x2) - d ] / SE
t = - 3.053
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 3.053.
Therefore, the P-value in this analysis is 0.002.
Interpret results. Since the P-value (0.002) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that people solves puzzeles more quickly in a red environment than in a blue one.
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