Assume that the paired data came from a population that is n

Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level find the mean value of the differences d for the paired sample data, the standard deviation of the differences d for the paried sample data, the t test statistic, and the critical values to test the claim that ?d=0.

xi 10, 7, 12, 12, 14, 12, 13, 10

yi 5, 6, 14, 11, 13, 13, 10, 10

Solution

Null hypothesis: ?d=0

Alternative hypothesis: ?d not equal to 0

The test statistic is

t= mean difference/(s/vn)

=1/(2.204/sqrt(8))

=1.28

It is a two-tailed test.

The degree of freedom =n-1=8-1=7

Given a=0.05, the critical values are t(0.025, df=7) =-2.36 or 2.36 (from student t table)

The rejection regions are if t<-2.36 or t> 2.36 , we reject the null hypothesis.

Since t=1.28 is between -2.36 and 2.36, we do not reject the null hypothesis.

So we can not conclude that there is the differences d for the paired sample data