You wish to test the following claim (HaHa) at a significance level of =0.001=0.

Question

You wish to test the following claim (HaHa) at a significance level of =0.001=0.001. For the context of this problem, d=PostTestPreTestd=PostTest-PreTestwhere the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your 11 and 22 are so that the differences are computed correctly.)

      Ho:d=0
      Ha:d0

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:

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

less than (or equal to)

greater than

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.

pre-test post-test 55.3 18.3 46.1 106.5 43.5 32.1 22.5 -24.7 34.9 34.5 46.1 87.7 45.5 36.1 41.7 -5.5 42.5 86.6 66.3 113.3 38.3 49.2 42.2 72.1 38.9 52.2 39.7 88.2 41.2 16.1 39.7 83.8

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between pre-test and post-test
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

Test statistic = -1.1084

p - Value = 0.2851

p - value is greater than

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

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.

Difference Mean Std. Err. DF T-Stat P-value pre-test - post-test -10.13125 9.1401574 15 -1.1084328 0.2851

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