IMathAS-libretexts

You wish to test the following claim ( $\displaystyle {H}_{{a}}$ ) at a significance level of $\displaystyle \alpha={0.05}$ . $\displaystyle {d}$ denotes the mean of the difference between pre-test and post-test scores.

$\displaystyle {H}_{{o}}:\mu_{{d}}={0}$
$\displaystyle {H}_{{a}}:\mu_{{d}}>{0}$

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
60.1	79.3
53.7	58.1
26.8	30.8
38.5	34.4
30.8	49.6
61.1	93.2
25.7	29.7
31.7	37.2
30.8	33.5
35.4	47.4
29.4	29.9
17.9	33.7
44.2	39.5
56.2	76.3
44.2	56.5
39.6	36.6
53.2	69.4
41.1	47
52.6	93.3
46.6	42.5
31.3	44

In StatCrunch:

Select Data --> Load data --> From paste
Paste the data above into the white space with the column titled included
Select Load Data
Select Stat --> T Statistics --> Paired
Choose the appropriate column for Sample 1 and 2 so that you are estimating the improved post-test score: $\displaystyle \mu_{{2}}-\mu_{{1}}$
Choose the appropriate alternative hypothesis
Select Compute!

What is the test statistic for this sample?

test statistic = Round to 3 decimal places.
What is the p-value for this sample? Round to 4 decimal places.

p-value =
The p-value is...
- less than (or equal to) $\displaystyle \alpha$
- greater than $\displaystyle \alpha$
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.

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