Sketch a diagram of the T distribution, indicate the areas of rejection and posi
ID: 3127825 • Letter: S
Question
Sketch a diagram of the T distribution, indicate the areas of rejection and position of the sample mean. An equational psychologist want to check the claim that regular physical exercise improves academic achievement. To control for academic aptitude, pairs of college students with similar GPAs were randomly assigned to either a treatment group that attached daily exercise classes or a control group that did not attend classes. At the end of the experiment, the following GPAs were recorded for the 7 pairs of participants: Test the null hypothesis at the.01 level of significance.Explanation / Answer
Here are the differences:
0.25
-0.07
0.23
0.44
0.21
0.35
0.15
Let ud = u(excercise) - u(no excercise).
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
At level of significance = 0.01
As we can see, this is a right tailed test.
Calculating the standard deviation of the differences (third column):
s = 0.165199604
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.062439581
Calculating the mean of the differences (third column):
XD = 0.222857143
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 3.569164601
As df = n - 1 = 6
Then the critical value of t is
tcrit = + 3.142668403
Also, using p values,
p = 0.005898027
As t > 3.1426, and P < 0.01, WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence at 0.01 level that regular physical exercise improve academic achievement. [CONCLUSION]
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