To test the effect of a physical fitness course on one\'s physical ability, the
ID: 3437695 • Letter: T
Question
To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in 1 minute, both before and after the course, was recorded. Ten randomly selected participants scored as shown in the following table. Can you conclude that a significant amount of improvement took place? Use = 0.01 and assume normality.
(a) Find t. (Give your answer correct to two decimal places.)_______
(ii) Find the p-value. (Give your answer correct to three decimal places.)________
(b) State the appropriate conclusion.
Before 11 12 13 15 16 20 21 17 11 11 After 13 16 24 25 20 17 23 22 20 14Explanation / Answer
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
At level of significance = 0.01
As you can see, this is a 1 tailed test.
Calculating the standard deviation of the differences (third column):
s = 4.270050741
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.350308607
Calculating the mean of the differences (third column):
XD = 4.7
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 3.480685805 [PART A]
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As df = n - 1 = 9
Then the critical value of t is
tcrit = 2.821437925
Thus, comparing t and tcrit, we WE REJECT THE NULL HYPOTHESIS.
Also, using p values,
p = 0.003465533 [PART A, II]
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There is a significant amount of improvement on the number of sit-ups per minute. [ANSWER, CONCLUSION, B]
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