Answer:
About 0.72
Step-by-step explanation:
Given the data:
With device : 22.6, 23.4, 28.4, 29, 29.3, 20.0
Without device :26.9, 24.4, 20.8, 20.8, 20.2, 26.0, 28.1, 25.6
Using calculator:
With device data:
Sample size (n1) = 6
Degree of freedom (df1) = 6 - 1 = 5
Mean(m1) = 25.45
Variance (s²1) = 15.631
Without device data:
Sample size (n2) = 8
Degree of freedom (df2) = n - 1 = 7
Mean (m2) = 24.1
Variance (s²2) = 9.54
s²t = ((df1/(df1 + df2)) * s²1) + ((df2/(df1 + df2)) * s²2)
s²t = ((5/(5+7)*15.63) + ((7/(5+7))*9.54)
= ((5/12) * 15.63) + ((7/12) * 9.54) = 12.0775
s²m1 = s²t/n1 = 12.0775/6 = 2.0123
s²m2 = s²t/n2 = 12.0775/8 = 1.511
T - statistic :
Tstat = (m1 - m2)/√(s²m1 + s²m2)
Tstat = (25.45 - 24.10) / √(2.0123 + 1.511)
Tstat= 1.350/√3.5233
Tstat = 1.350 / 1.8770455
Tstat = 0.7192153 = 0.72
