Question

You wish to test the following claim (H1H1) at a significance
level of α=0.002α=0.002. For the context of this problem,
d=x2−x1d=x2-x1 where the first data set represents a pre-test and
the second data set represents a post-test.

Ho:μd=0Ho:μd=0

H1:μd≠0H1: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=14n=14 subjects. The average
difference (post - pre) is ¯d=−13.2d¯=-13.2 with a standard
deviation of the differences of sd=21.4sd=21.4.

What is the critical value for this test? (Report answer accurate
to three decimal places.)

critical value = ±±

What is the test statistic for this sample? (Report answer accurate
to three decimal places.)

test statistic =

The test statistic is...

- in the critical region
- not in the critical region

This test statistic leads to a decision to...

- reject the null
- accept the null
- fail to reject the null

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.

- Question Help:
*Message*Message instructor

Answer #1

This is two tailed test, for α = 0.002 and df = 13

Critical value of t are -3.852 and 3.852.

Hence reject H0 if t < -3.852 or t > 3.852

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (-13.2 - 0)/(21.4/sqrt(14))

t = -2.308

The test statistic is...not in the critical region

This test statistic leads to a decision to..fail to reject the
null

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

You wish to test the following claim (H1H1) at a significance
level of α=0.10α=0.10. For the context of this problem,
d=x2−x1d=x2-x1 where the first data set represents a pre-test and
the second data set represents a post-test.
Ho:μd=0Ho:μd=0
H1:μd>0H1:μd>0
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distributed, but you do not know the standard deviation. You obtain
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You wish to test the following claim (HaHa) at a significance
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the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
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the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
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56.3
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57.7
58.7
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42.6
51
23
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