You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10. For the context of this problem,
μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and
the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
the following sample of data:
pre-test | post-test |
---|---|
56.3 | 79.6 |
61.1 | 80.6 |
55.5 | 57.7 |
58.7 | 72.7 |
60.2 | 42.6 |
51 | 23 |
56.3 | 51.5 |
a.What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value = ±±
b.What is the test statistic for this sample? (Report answer
accurate to three decimal places.)
test statistic =
c.The test statistic is...
in the critical region
not in the critical region
d.This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null
e. As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.
P/s. If you can show me how to use calculator, it would be great.
The statistical software output for this problem is:
Paired T hypothesis test:
μD = μ1 - μ2 : Mean of the
difference between post-test and pre-test
H0 : μD = 0
HA : μD ≠ 0
Hypothesis test results:
Difference | Mean | Std. Err. | DF | T-Stat | P-value |
---|---|---|---|---|---|
post-test - pre-test | 1.2285714 | 7.286998 | 6 | 0.16859774 | 0.8717 |
Hence,
a) Critical value = 1.943
b) Test statistic = 0.169
c) is not in the critical region
d) Fail to reject the null
e) There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.
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