You wish to test the following claim (Ha) at a significance level of = 0.002. Fo

Question

You wish to test the following claim (Ha) at a significance level of = 0.002. For the context of this problem, d=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: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? (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?  

pre-test post-test 29.6 39.4 34.8 31.5 44.1 22.3 21.2 -1.8 38 33.7 34.8 22.4 46.7 47.8 39.7 58.1 49.2 32.8 35.9 33 37.7 35.5 36.1 12.5 47.4 53.6 46.1 31.2 63.3 61.9 28.7 11.5 36.1 17.2 38.2 42.1 43.6 10.1 22.5 9.4 41 27.6 28.3 35.8 16.7 -22.7 44.4 42.6 16.7 27.5

Explanation / Answer

Given that,

null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.064
since our test is two-tailed
reject Ho, if to < -2.064 OR if to > 2.064
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
pooled variance = calculate value of Sd= S^2
to = d/ (S/n) = 2.885
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.885 ) = .0082

0.0000 hypothesized value 36.8320 mean pre-test 28.6000 mean post-test 8.2320 mean difference (pre-test - post-test) 14.2898 std. dev. 2.8580 std. error 25 n 24 df 2.88 t .0082 p-value (two-tailed)

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