t test in written way

1. T – TEST

2. Find the t – value
X1 X2
3 20
3 13
3 13
12 20
15 29
16 32
17 23
19 20
23 25
24 15
32 30
S.D ?
a) 6.365
b) 8.183
c) 8.103
d) 8.334
T ?
a) 1.256
b) 1.231
c) 1.895
d) 1.985

3. SOLUTION
X1 = 3+3+3+12+15+16+17+19+23+24+32
11
X1 = 167
11
X1 = 15.18
X2 = 20+13+13+20+29+32+23+20+25+15+30
11
X2 = 240
11
X2 = 21.81

4. NO. X1 X2 X1 – X1 (X1 – X1) (X2 – X2) (X2 – X2)
1 3 20 12.18 148.3524 1.81 3.2761
2 3 13 12.18 148.3524 8.81 77.6161
3 3 13 12.18 148.3524 8.81 77.6161
4 12 20 3.18 10.1124 1.81 3.2761
5 15 29 0.18 0.0324 7.19 51.6961
6 16 32 0.82 0.6724 10.19 103.8361
7 17 23 1.82 3.3124 1.19 1.4161
8 19 20 3.82 14.5924 1.18 1.3924
9 23 25 7.82 61.1524 3.19 10.1761
10 24 15 8.82 77.7924 6.81 46.3761
11 32 30 16.82 282.9124 8.19 67.0761
TOTAL X1 = 167 X2 = 240 = 895.6364 = 443.7534
2 2

5. S.D = ∑(X1 – X1) + ∑(X2 – X2)
N1 + N2 – 2
S.D = 895.6364 + 443.7534 = 1339.3898 = 66.96949
11 + 11 – 2 20
S.D = 8.183
T = X1 – X2 N1*N2 = 15.18 – 21.81 11*11 = 6.63 121
S.D N1 + N2 8.183 11 + 11 8.183 22
T = 0.810 5.5 = 0.810 * 2.34
T = 1.8954
2 2

6. THANK YOU