Answer
Reject Null hypothesis
Work Step by Step
First we need to calculate difference of population 1 and population 2:
19 - 24 = -5
25 - 27 = -2
31 - 36 = -5
52 - 53 = -1
49 - 55 = -6
34 - 34 = 0
59 - 66 = -7
47 - 51 = -4
17 - 20 = -3
51 - 55 = -4
$\bar x_{d} = \frac{-5 + .... + (-4)}{10} = -3.7$
$s^{2}_{d} = \frac{(-5 - (-3.7))^2 + .... + (-4 - (-3.7))^{2}}{10 - 1} = 2.2136 $
$t = \frac{-3.7}{2.2136/\sqrt 10} = \frac{-3.7}{0.7} = 0.7 = -5.2857$
df = n - 1 = 10 - 1 = 9
$t_{α} = 0.10$
From student's t distribution table, we have:
$t_{0.10} = 1.383$
Since -5.2857 < 1.383, we reject Null hypothesis
