Sketch the sampling distribution and show the area corresponding to the P-value. ^ 0 -2 O O -2 2 t (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 a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. a (v) Interpret your conclusion in the context of the application. O 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. O 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. O 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. O 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 ₁-₂. (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. O 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. O 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. O 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. O Because the interval contains only negative numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies i higher in region II.

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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Sketch the sampling distribution and show the area corresponding to the P-value.
^
0
-2
O
O
-2
2
t
(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 a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
a
(v) Interpret your conclusion in the context of the application.
O 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.
O 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.
O 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.
O 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 ₁-₂. (Round your answers to two decimal places.)
lower limit
upper limit
Explain the meaning of the confidence interval in the context of the problem.
O 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.
O 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.
O 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.
O Because the interval contains only negative numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies i higher in region II.
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. ^ 0 -2 O O -2 2 t (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 a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. a (v) Interpret your conclusion in the context of the application. O 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. O 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. O 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. O 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 ₁-₂. (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. O 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. O 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. O 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. O Because the interval contains only negative numbers, this indicates that at the 95% confidence level, the number of cases of fox rabies i higher in region II.
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 9 9 9 7 8 8 1
3 3 3 2 5 14 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 16 8 5 4
4 2 2 5 6 9
USE SALT
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 four decimal places.)
51
x₂ =
$2²
(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.
O Hot H₁ = H₂² H₁² H₁ # H₂
O Ho H₁ H₂ Hqi Hy <H₂
O Hoi H₁ H₂ Hqi Hy
·1₂
O Hoi Hy > H₂? H₂i H₂ = H₂
(ii) What sampling distribution will you use? What assumptions are you making?
O The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
O 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? Compute the corresponding z or t value as appropriate. (Test the difference ₁ - M₂. Do not use rounded values. Round your final answer to three decimal places.)
(iii) Find (or estimate) the P-value.
OP-value> 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
OP-value < 0.010
Transcribed Image Text: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 9 9 9 7 8 8 1 3 3 3 2 5 14 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 16 8 5 4 4 2 2 5 6 9 USE SALT 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 four decimal places.) 51 x₂ = $2² (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. O Hot H₁ = H₂² H₁² H₁ # H₂ O Ho H₁ H₂ Hqi Hy <H₂ O Hoi H₁ H₂ Hqi Hy ·1₂ O Hoi Hy > H₂? H₂i H₂ = H₂ (ii) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O 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? Compute the corresponding z or t value as appropriate. (Test the difference ₁ - M₂. Do not use rounded values. Round your final answer to three decimal places.) (iii) Find (or estimate) the P-value. OP-value> 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 OP-value < 0.010
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