8. A psychologist had a theory that exposing young children to a program which f
ID: 3360664 • Letter: 8
Question
8. A psychologist had a theory that exposing young children to a program which fostered creati thinking would lead to better performance on a creative problem solving test (higher score is better). To test this theory, he used a random sample of 6 sets of identical twins. One of each paitr was placed in a creative thinking program, and the other was not (control group). A test ve Twin Pair | 52 | 36- 13 | 24 | 35 46 Experimental Group 40 32 14 41 a. What is the null hypothesis? b. Is this a 1-or 2-tailed test? Why? Do we reject or fail to reject (accept) the null hypothesis (at alpha 0.01)? c.
Explanation / Answer
a.
Null Hypothesis H0: The mean difference score of creative problem solving test of students attending the program and the score of students not attending the program is 0
b.
The claim is that the mean difference score of creative problem solving test of students attending the program and the score of students not attending the program is greater than 0. As, we are testing for one side (greater than) this is a one-tail test.
c.
We will be conductiong matched-pairs t-test.
The difference in the score of experimental and control group is,
12, 4, -1, 2, 6, 5
The mean difference of experimental and control group is 4.67
The standard deviation of difference of experimental and control group is 4.37
Standard error of the difference = SD / sqrt(n) = 4.37 / sqrt(6) = 1.78
Test statistic t = Mean difference / SE = 4.67 / 1.78 = 2.62
Degree of freedom = n -1 = 6-1 = 5
P-value for t = 2.62 and df = 5 is 0.0235
As, p-value (0.0235) is greater than the significance level of (0.01) ,we fail to reject the null hypothesis and conclude that at 0.01 level of signficance, there is no significant statistical difference between score of creative problem solving test of students attending the program and the score of students not attending the program.
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