Polychlorinated biphenyls PCB are worldwide environmental co

Polychlorinated biphenyls (PCB) are worldwide environmental contaminants of industrial origin that are related to DDT. They are being phased out in the United States, but they will remain in the environment for many years. An experiment is run to study the effects of PCB on the reproductive ability of screech owls. The purpose is to compare the shell thickness of eggs produced by birds exposed to PCB to that of birds not exposed to the contaminant. It is thought that shells of the former group will be thinner than those of the latter. Do these data support this research hypothesis? Explain.

Solution

Set Up Hypothesis
Null Hypothesis, There Is NoSignificance between them Ho: u1 > u2
Alternative Hypothesis, There Is Significance between themH1: u1 < u2
Test Statistic
X (Mean)=0.21; Standard Deviation (s.d1)=0.0334
Number(n1)=9
Y(Mean)=27.3276; Standard Deviation(s.d2)=76.6392
Number(n2)=9
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (8*0.0011 + 8*5873.567) / (18- 2 )
S^2 = 2936.784
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=0.21-27.3276/Sqrt((2936.784( 1 /9+ 1/9 ))
to=-27.1176/25.5464
to=-1.0615
| to | =1.0615
Critical Value
The Value of |t | with (n1+n2-2) i.e 16 d.f is 1.746
We got |to| = 1.0615 & | t | = 1.746
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -1.0615 ) = 0.15211
Hence Value of P0.05 < 0.15211,Here We Do not Reject Ho