A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 2 7 7 7 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 1 3 4 3 3 8 5 4 4 4 2 2 5 6 9 (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 = μ2 H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 < μ2 (ii) What sampling distribution will you use? What assumptions are you making? The Student's t. 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 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 unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)(iii) Find the P-value. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value. (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? Since the P-value ≤ α, we reject H0. The data are statistically significant. Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant. Since the P-value > α, we fail to reject H0. The data are not statistically significant. (v) Interpret your conclusion in the context of the application. Reject H0. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Fail to reject H0. At the 5% level of significance, the evidence is insufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Fail to reject H0. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Reject H0. At the 5% level of significance, the evidence is insufficient to indicate 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. At the 95% level of confidence, we can conclude that the number of cases of fox rabies differs between the two regions. At the 95% level of confidence, we cannot conclude that the number of cases of fox rabies differs between the two regions.

A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 2 7 7 7 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 1 3 4 3 3 8 5 4 4 4 2 2 5 6 9 (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 = μ2 H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 < μ2 (ii) What sampling distribution will you use? What assumptions are you making? The Student's t. 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 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 unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)(iii) Find the P-value. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value. (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? Since the P-value ≤ α, we reject H0. The data are statistically significant. Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant. Since the P-value > α, we fail to reject H0. The data are not statistically significant. (v) Interpret your conclusion in the context of the application. Reject H0. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Fail to reject H0. At the 5% level of significance, the evidence is insufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Fail to reject H0. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions. Reject H0. At the 5% level of significance, the evidence is insufficient to indicate 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. At the 95% level of confidence, we can conclude that the number of cases of fox rabies differs between the two regions. At the 95% level of confidence, we cannot conclude that the number of cases of fox rabies differs between the two regions.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n₁ = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location.

x₁: Region I Data

2	7	7	7	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

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

(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 = μ₂

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

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

The Student's t. 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 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 unknown standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

(iii) Find the P-value. (Round your answer to four decimal places.)

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

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

Since the P-value ≤ α, we reject H₀. The data are statistically significant.

Since the P-value ≤ α, we fail to reject H₀. The data are statistically significant.

Since the P-value > α, we reject H₀. The data are not statistically significant.

Since the P-value > α, we fail to reject H₀. The data are not statistically significant.

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

Reject H₀. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions.

Fail to reject H₀. At the 5% level of significance, the evidence is insufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions.

Fail to reject H₀. At the 5% level of significance, the evidence is sufficient to indicate that there is a difference in the mean number of cases of fox rabies between the two regions.

Reject H₀. At the 5% level of significance, the evidence is insufficient to indicate 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.

At the 95% level of confidence, we can conclude that the number of cases of fox rabies differs between the two regions.

At the 95% level of confidence, we cannot conclude that the number of cases of fox rabies differs between the two regions.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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