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	6	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	4	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?


State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂H₀: μ₁ > μ₂; H₁: μ₁ = μ₂    H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations.    The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Do not use rounded values. Round your final answer to three decimal places.)

Answer 1

(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.)

$\bar{x}_{1}$	$4.94$
$s_{1}$	$2.95$
$\bar{x}_{2}$	$4.27$
$s_{2}$	$2.19$

(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: The level of significance is 0.05

State the null and alternative hypotheses.

Answer: H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

(b) What sampling distribution will you use? What assumptions are you making?

Answer: The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Do not use rounded values. Round your final answer to three decimal places.)

Answer: The value of the sample test statistic is:

$\large t=0.722$

Explanation:

We can use the excel data analysis tool to run t-Test: Two-Sample Assuming Unequal Variances. The excel output is given below:

	Sample 1	Sample 2
Mean	4.9375	4.266666667
Variance	8.729166667	4.780952381
Observations	16	15
Hypothesized Mean Difference	0
df	28
t Stat	0.722
P(T<=t) one-tail	0.238269256
t Critical one-tail	1.701130908
P(T<=t) two-tail	0.476538513
t Critical two-tail	2.048407115

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