Question

Control of the disease caused by the Eastern Equine Encephalomyelitis (EEE) virus requires a good understanding of which vectors are most important in transmitting the EEE virus to the different hosts. There are six species of mosquitoes in Alabama carrying this virus. A DNA analysis of a sample of blood-engorged female mosquitoes of the species Ae. vexans shows that 48 of the n=127 mosquitoes have fed on mammals.

Use the R function binom.test() to find the following 92% confidence intervals for the proportion of blood meals taken from mammals by the species Ae. vexans.

(a) The 92% two-sided confidence interval ranges from __________ to __________.

(b) The 92% lower-bound confidence interval ranges from _________ to 1.

(c) The 92% upper-bound confidence interval ranges from 0 to __________.

Now calculate the following confidence intervals using the R function prop.test().

(d) The 92% two-sided confidence interval ranges from _________ to _________ .

(e) The 92% lower-bound confidence interval ranges from _________  to 1.

(f) The 92% upper-bound confidence interval ranges from 0 to _________.

Answer 1

a) n<-127
p<-48/127
x<-48
binom.test(x,n,p,alternative = c("two.sided"),conf.level = .92)

Using the above code you will get the result:

92 percent confidence interval:
0.3017543 to 0.4589727

b) We have to find out the lower bound, so we will have to find a number such that the probability remains greater than that number

n<-127
p<-48/127
x<-48
binom.test(x,n,p,alternative = c("greater"),conf.level = .92)

The result would be:

.92 percent confidence interval:
0.3156476 to 1.0000000

c) Similarly we shall find out a number such that the probability is less than that number.

n<-127
p<-48/127
x<-48
binom.test(x,n,p,alternative = c("less"),conf.level = .92)

We will have the following result:

92 percent confidence interval:
0.0000000 to 0.4436474

d)n<-127
p<-48/127
x<-48
prop.test(x,n,p,alternative = c("two.sided"),conf.level = .92)

Result:

92 percent confidence interval:
0.3063414 to 0.4553161

e) n<-127
p<-48/127
x<-48
prop.test(x,n,p,alternative = c("greater"),conf.level = .92)

Result:

92 percent confidence interval:
0.3198021 to 1.0000000

f) n<-127
p<-48/127
x<-48
prop.test(x,n,p,alternative = c("less"),conf.level = .92)

Result:

92 percent confidence interval:
0.0000000 to 0.4398398