Conservationists are interested in the effect of an oil spill on the rocky shore

Question

Conservationists are interested in the effect of an oil spill on the rocky shore populations of São Sebastião, Brazil. They are using a species of barnacle as their biological indicator; Chthamalus spp. Data were collected from 17 stations, and at each station, within a homogenous portion of the shore, the density of the barnacle species was estimated from the center of the barnacle belt. From 1992 to 1994, eight samples were taken before the spill at each station. The spill occurred on 15 May 1994, five additional measurements were taken between then and 1995. The spill did not affect all stations, and these locations were designated as impact sites. Before the spill occurred the sampled mean difference between the control and impact sites was -5.53 barnacles ft-1 with a sample variance of 45.82. After the oil spill occurred the sampled mean difference between the control and impact sites was -10.24 barnacles ft-1 with a sample variance of 98.63.

a) Assess the evidence that the oil spill had an effect on the density of barnacles on the rocky shores.

b) Consider the way the data were collected. How might this have affected the results of the analysis?

c) There have been 191 oil spills in this area between 1974 and1994. How might this new information affect your conclusions and/or analysis?

Explanation / Answer

Given that,
mean(x)=-5.53
standard deviation , s.d1=6.769
number(n1)=8
y(mean)=-10.24
standard deviation, s.d2 =9.9312
number(n2)=13
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.895
since our test is right-tailed
reject Ho, if to > 1.895
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =-5.53--10.24/sqrt((45.81936/8)+(98.62873/13))
to =1.291
| to | =1.291
critical value
the value of |t | with min (n1-1, n2-1) i.e 7 d.f is 1.895
we got |to| = 1.29081 & | t | = 1.895
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.2908 ) = 0.11888
hence value of p0.05 < 0.11888,here we do not reject Ho

ANSWERS
---------------
a).we do not have enough support the the evidence that the oil spill had an effect on the density of barnacles on the rocky shores.
b)
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 1.291
critical value: 1.895
decision: do not reject Ho
p-value: 0.11888

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