# Stats- Two-tailed test

A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in the table below. Assume that the data are normally distributed in the population.

Pair Group1 Group2
1 10 12
2 8 9
3 11 11
4 8 10
5 9 12

a) At 10% level of significance and using a 2-tailed test, what is your conclusion?

D (Group1 - Group2) D^2
2 4
1 1
0 0
2 4
3 9
D= 8 D^2=18

X= 8/5= 1.6
S^2 = 18- ((8^2)/5)/(5-1) = 1.3--> S= 1.14

H0: M=0
H1: M>0

Reject H0 if t>2.1319

t= (1.6-0) / (1.14/5(sqroot)) = 3.14

There is enough evidence.

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