SOLUTION: You wish to test the following claim (Ha) at a significance level of α=0.05. For the context of this problem ,μd = μ2 − μ1 where the first data set represents a pre-test and

Question 1134328: You wish to test the following claim (Ha) at a significance level of α=0.05. For the context of this problem ,μd = μ2 − μ1 where the first data set represents a pre-test and the second data set represents a post-test.
Ho:μd=0
Ha:μd>0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=19 subjects. The average difference (post - pre) is d=5 (Note: d has a horizontal bar over it) with a standard deviation of the differences of sd=10.4.
1. What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

2. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
3. The test statistic is...
(a) in the critical region
(b) not in the critical region

4. This test statistic leads to a decision to...
(a) reject the null
(b) accept the null
(c) fail to reject the null
5. As such, the final conclusion is that...
(a) There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
(b) There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
(c) The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
(d)There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a paired t-test with tdf=18,0.95, upper tail probability, value of t being 1.734
and the test statistic is t=5/10.4/sqrt(19), which is 2.096, in the critical region. (t>1.734)
reject Ho with p-value 0.0252
c
Ho is claiming that the mean difference is 0 (or less than 0).
Ha is claiming that the mean difference is greater than 0.
We reject Ho (that the mean difference is <=0) and conclude that the mean difference is >0.

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