Persons having Raynauds syndrome are apt to suffer a sudden

Persons having Raynaud\'s syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm^2/min) was measured. For m = 8 subjects with the syndrome, the average heat output was x = 0.63, and for n = 8 nonsufferers, the average output was 2.08. Let mu_1 and mu_2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with sigma_1 = 0.3 and sigma_2 = 0.4. Consider testing H_0: mu_1 - mu_2 = -1.0 versus H_a: mu_1 - mu_2

Solution

Set Up Hypothesis
Null Hypothesis ,there Is No-Significance between them Ho: u1 - u2 = -1.0
Alternate Hypothesis , there Is Significance between them H1: u1 - u2 < -1.0
Test Statistic
X(Mean)=0.63
Standard Deviation(s.d1)=0.3
Number(n1)=8
Y(Mean)=2.08
Standard Deviation(s.d2)=0.4
Number(n2)=8
we use Test Statistic (Z) = (X-Y)-(U1-U2)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=(0.63-2.08)-(-1.0)/Sqrt((0.09/8)+(0.16/8))
Zo =-2.55
| Zo | =2.55
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo | =2.545 & | Z | =2.326
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail - Ha : ( P < -2.55 ) = 0.00546
Hence Value of P0.01 > 0.00546,Here we Reject Ho