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

1	8	8	8	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

1	1	5	1	6	8	5	4
4	4	2	2	5	6	9

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	=

(a) 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.)(i) 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

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

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.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.

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


(iii) Find (or estimate) the P-value.

P-value > 0.5000.250 < P-value < 0.500    0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(iv) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(v) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that there is a difference in the mean number of cases of fox rabies between the two regions.Reject the null hypothesis, there is sufficient evidence that there is a difference in the mean number of cases of fox rabies between the two regions.    Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in the mean number of cases of fox rabies between the two regions.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in the mean number of cases of fox rabies between the two regions.

(b) Find a 95% confidence interval for

μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit
upper limit

Explain the meaning of the confidence interval in the context of the problem.

Because the interval contains only positive numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies is higher in region I.Because the interval contains both positive and negative numbers, this indicates that at the 95% confidence level, we cannot say that the number of cases of fox rabies differs between the two regions.     Because the interval contains both positive and negative numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies is higher in region I.Because the interval contains only negative numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies is higher in region II.

Answer 1