Question

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. 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
pre-test and post-test samples for n=22n=22 subjects. The average
difference (post - pre) is ¯d=25.6d¯=25.6 with a standard deviation
of the differences of sd=30.8sd=30.8.

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

test statistic =

What is the p-value for this sample? (Report answer accurate to
four decimal places.)

p-value =

The p-value is...

- less than (or equal to) αα
- greater than αα

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 greater than 0.
- 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.
- The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
- 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 #1

The statistical software output for this problem is:

Hence,

Test statistic = 3.899

P - value = 0.0004

The p - value is less than (or equal to) α

This test statistic leads to a decision to reject the null

As such, the final conclusion is that the sample data support
the claim that the mean difference of post-test from pre-test is
greater than 0. **Option C** is correct.

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. 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
pre-test and post-test samples for n=50n=50 subjects. The average
difference (post - pre) is ¯d=−6.7d¯=-6.7 with a standard deviation
of...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. For the context of this problem, the first
data set represents a pre-test and the second data set represents a
post-test. You'll have to be careful about the direction in which
you subtract.
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
pre-test and post-test samples for n=47n=47 subjects. The average
difference...

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01. 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
pre-test and post-test samples for n=50n=50 subjects. The average
difference (post - pre) is ¯d=−18.8d¯=-18.8 with a standard
deviation of the...

You wish to test the following claim (HaHa) at a significance
level of α=0.02α=0.02. 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
pre-test and post-test samples for n=14n=14 subjects. The average
difference (post - pre) is ¯d=−17.4d¯=-17.4 with a standard
deviation of the...

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01. 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
pre-test and post-test samples for n=12n=12 subjects. The average
difference (post - pre) is ¯d=7.1d¯=7.1 with a standard deviation
of the...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. dd denotes the mean of the
difference between pre-test and post-test
scores.
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:
post-test
pre-test
49.3
31.9
47.1
27.5
42.6
40.9
42.2
43.4
41.5
39.1
41.8
52.5
33.5
17
42.9
40.1
33.5
31.6
39.8
57.2
47.1
45.7
46.5
50.9
51.7
52.4...

You wish to test the following claim (HAHA) at a significance
level of α=0.01α=0.01. For the context of this problem,
μd=μ2−μ1μd=μ2-μ1 where the first data set represents pre-strike
production and the second data set represents post-strike
production.
Ho:μd=0Ho:μd=0
HA:μd<0HA:μd<0
You believe the population difference of production is normally
distributed, but you do not know the standard deviation. You obtain
pre-strike and post-strike production samples for n=6n=6 subjects.
The average difference (post - pre) is ¯d=−47.4d¯=-47.4 with a
standard deviation of...

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
pre-test and post-test samples for n=117n=117 subjects. The average
difference (post - pre) is ¯d=4d¯=4 with a standard deviation of
the...

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...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a
pre-test and the other data set represents a post-test. Each row
represents the pre and post test scores for an individual.
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
63.4
104.2
65.8
90...

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