Question

A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of

n₁ = 16

locations in region I gave the following information about the number of cases of fox rabies near that location.

x₁:

   Region I Data

2	9	9	9	7	8	8	1
3	3	3	2	5	1	4	6

A second random sample of

n₂ = 15

locations in region II gave the following information about the number of cases of fox rabies near that location.

x₂:

   Region II Data

2	2	5	2	6	8	5	4
4	4	2	2	5	6	9

(i) Use a calculator with sample mean and sample standard deviation keys to calculate x₁ and s₁ in region I, and x₂ and s₂ in region II. (Round your answers to two decimal places.)

x1	=
s1	=
x2	=
s2	=

(ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)
(a) What is the level of significance?

Answer 1

SolutionI)

use R software

mean and sd functions to find mean and standard deviations

Region1 <- c(2, 9 ,9, 9 ,7, 8, 8, 1, 3, 3 ,3, 2 ,5, 1, 4, 6)

x1 <- round(mean(Region1),2)

x1

s1 <- round(sd(Region1),2)

s1

x2 <- round(mean(Region2),2)

x2

s2 <- round(sd(Region2),2)

s2

output:

x1
[1] 5
> s1 <- round(sd(Region1),2)
> s1
[1] 2.99
> x2 <- round(mean(Region2),2)
> x2
[1] 4.4
> s2 <- round(sd(Region2),2)
> s2
[1] 2.23

x1	5
s1	2.99
x2	4.4
s2	2.23

(ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions

perform t test for difference in means

use t.test function in R software.

default level of signifance=0.05

t.test(Region1,Region2)

Output:

Welch Two Sample t-test

data: Region1 and Region2
t = 0.63608, df = 27.653, p-value = 0.53
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-1.333296 2.533296
sample estimates:
mean of x mean of y
5.0 4.4

t=0.636

p=0.53

p>0.05

Fail to reject H0.

There is no sufficient statistical evidence at 5% leve of signifcance to conclude that

there is a difference (either way) in the mean number of cases of fox rabies between the two regions

(a) What is the level of significance?

alpha=0.05