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 40 of the n=131 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 1.1.

(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 1.1.

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

Answer 1

a)

> binom.test(40,131,conf.level=0.92,alternative="two.sided")

   Exact binomial test

data: 40 and 131
number of successes = 40, number of trials = 131, p-value = 9.796e-06
alternative hypothesis: true probability of success is not equal to 0.5
92 percent confidence interval:
0.2353780 0.3827826
sample estimates:
probability of success
0.3053435

(a) The 92% two-sided confidence interval ranges from 0.2354 to 0.3829

b)

> binom.test(40,131,conf.level=0.92,alternative="greater")

   Exact binomial test

data: 40 and 131
number of successes = 40, number of trials = 131, p-value = 1
alternative hypothesis: true probability of success is greater than 0.5
92 percent confidence interval:
0.2479514 1.0000000
sample estimates:
probability of success
0.3053435

(b) The 92% lower-bound confidence interval ranges from 0.24795 to 1.

c)

> binom.test(40,131,conf.level=0.92,alternative="less")

   Exact binomial test

data: 40 and 131
number of successes = 40, number of trials = 131, p-value = 4.898e-06
alternative hypothesis: true probability of success is less than 0.5
92 percent confidence interval:
0.0000000 0.3679913
sample estimates:

probability of success
0.3053435

(c) The 92% upper-bound confidence interval ranges from 0 to 0.36799

d)

> prop.test(40,131,conf.level=0.92,alternative="two.sided")

   1-sample proportions test with continuity correction

data: 40 out of 131, null probability 0.5
X-squared = 19.084, df = 1, p-value = 1.251e-05
alternative hypothesis: true p is not equal to 0.5
92 percent confidence interval:
0.2365272 0.3835357
sample estimates:
p
0.3053435

(d) The 92% two-sided confidence interval ranges from 0.2365 to 0.3835

e)

> prop.test(40,131,conf.level=0.92,alternative="greater")

   1-sample proportions test with continuity correction

data: 40 out of 131, null probability 0.5
X-squared = 19.084, df = 1, p-value = 1
alternative hypothesis: true p is greater than 0.5
92 percent confidence interval:
0.2484777 1.0000000
sample estimates:
p
0.3053435
(e) The 92% lower-bound confidence interval ranges from 0.2485 to 1.

f)

> prop.test(40,131,conf.level=0.92,alternative="less")

   1-sample proportions test with continuity correction

data: 40 out of 131, null probability 0.5
X-squared = 19.084, df = 1, p-value = 6.255e-06
alternative hypothesis: true p is less than 0.5
92 percent confidence interval:
0.0000000 0.3683761
sample estimates:
p
0.3053435

(f) The 92% upper-bound confidence interval ranges from 0 to 0.3684