You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. For the context of this problem, one data set represents a pre-test and the other 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=329n=329 subjects. The average difference (post - pre) is ¯d=−1.8d¯=-1.8 with a standard deviation of the differences of sd=32.9sd=32.9.
given data are
sample n=329
average difference =-1.8
standard deviation of the difference sd=32.9
null hypothesis H0: - =0
alternative hypothesis Ha :-
= level of significance =0.005
test statistic :- t=
t= -1.8/(32.9/)
= -1.8 / 1.8138
=-0.9924
at df= n-1 =328 in 2 tail p value is
2× p (t= -0.9924)=2 ×0.16087
= 0.32174 = 0.3217
decision:- the p value is greater than so fail to reject the null hypothesis H0 .
conclusion:- 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
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