Initial Level (i)
Final Level (f)
d=i–f
184
191
-7
49
219
206
13
169
189
185
4
16
196
214
-18
324
198
190
8
64
196
192
4
16
186
194
-8
64
206
195
11
121
219
208
11
121
201
190
11
121
205
185
20
400
Total = 49
Total = 1465
Sd = 11.253
Sd = 9.169
Mean = 199.91
Mean = 195.45
SD pooled = sqrt ((11 - 1)* 11.253^2 + (11 - 1) * 9.169^2) / (11 + 11 - 2)
SD pooled = sqrt (10* 126.63 + 10 * 84.07) / 20
SD pooled = 10.264
d = mean difference = 4.46
Now, we calculate t value at df = 20 and alpha/2 = 0.05 (since 90% confidence)
d^2
t value = 1.7247
The 90% Confidence interval = d - t * (SD / sqrt (1/n1 + 1/n2)), where, t denotes t critical at
alpha/2 and df = n1 + n2 – 1, d is mean difference, and SD is standard deviation of difference.
CI = (199.91 – 195.45) – 1.7247 * 10.264 * sqrt (1/11 + 1/11), (199.91 – 195.45) + 1.7247 * 10.264 * sqrt
(1/11 + 1/11)
CI = 4.46 – 17.70 * 0.4264, 4.46 + 17.70 * 0.4264
CI = (-3.1, 12)