Complete question :
A : 2.7, 3.7, 5.6, 2.6, 2.7
B : 5.1, 4.0, 3.9, 3.8, 5.2
Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89
Answer: A.1.73
Step-by-step explanation:
Given the data:
A : 2.7, 3.7, 5.6, 2.6, 2.7
B : 5.1, 4.0, 3.9, 3.8, 5.2
Difference betweenA and B (A - B) :
Xd = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5
Sum of (A - B) = Σ Xd = (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7
Md = ΣXd / n = - 4.7 / 5 = - 0.94
Xd - Md = (-2.4 + 0.94), (-0.3 + 0.94), (1.7 + 0.94), (-1.2 + 0.94), (-2.5 + 0.94)
(Xd - Md) = - 1.46, 0.64, 2.64, - 0.26, - 1.56
(Xd - Md)^2 = (-1.46)^2 + 0.64^2 + 2.64^2 + (-0.26)^2 + (-1.56)^2
Σ(Xd - Md)^2 = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012
Standard deviation = √[Σ(Xd - Md)^2 / (n-1)]
Standard deviation= √12.012 / 4
Standard deviation = 1.7329
Standard deviation= 1.73
