Question

Q. It was thought that at a particular point in time 15% of the rabbit population in a region was infected by RHDV1-K5 virus. At the time a researcher trapped 25 rabbits from this region and had each tested to see if it carries virus. The number of rabbits in this sample with the virus is denoted by V.

a) Write down the possible values of V.

b) State a suitable distribution for V and provide the parameter(s) for the distribution.

c) Determine the Expected value of V and interpret this value in context to the research.

d) USe and show manual calculation to determine the probability that at least 2 rabbits have the virus.

e) It transpired that 20 of the rabbit did in fact carry the virus. Use R commander to determine the probability that 20 or more rabbit will have the virus.

f) Considering your answer to part e), say if this casts doubt on the original understanding of the prevalence of the virus in this region at that point in time. Give brief explanation.  

Answer 1

A.

Possible Values of V = {1,2,3....,25}

B.

V can be described by using the Binomial distribution with n = 25 and probability of success, p being 0.15

C.

Expected Value of V = n*p

= 25*0.15

= 3.75

Expected Value of V tells us that if take a large no. of 25 rabbit samples and compute the no. of rabbits infected with the virus in each sample then the mean of all those no. will be 3.75.

D.

We know that,

P(X=x) = (nCx)*p^x*(1-p)^n-x

So,

P(X2) = 0.907

E.

P(X20) ~ 0

F.

H₀: p = 0.15

H₁: p > 0.15

= 20/25

= 0.8

= = 0.8

=

= 0.0714

z = (-p)/

= (0.8-0.15)/0.0714

= 9.10

p-value ~ 0 < 0.05 i.e. we can reject H₀ and hence we say that this new sample does caste doubt on our understanding of prevalence of the virus in this region at that point in time.

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