1. Answer the following questions using the differences D1, ., D20 shown in Figure 2. (a) Test the hypothesis that the mean U.S. mortality rate Op remained the same or increased from 2005 to 2015 against the alternative that the mean mortality rate decreased. State the hypotheses, test statistic, rejection region, and p-value. Interpret the conclusion of the test at level a = 0.01. (b) Calculate the power of the test you performed in the previous part at 0p = -10. What is the type II error rate for this alternative scenario? (c) Compute a 99% confidence interval for the change in mean heart rate mortality. Interpret the interval in context.
1. Answer the following questions using the differences D1, ., D20 shown in Figure 2. (a) Test the hypothesis that the mean U.S. mortality rate Op remained the same or increased from 2005 to 2015 against the alternative that the mean mortality rate decreased. State the hypotheses, test statistic, rejection region, and p-value. Interpret the conclusion of the test at level a = 0.01. (b) Calculate the power of the test you performed in the previous part at 0p = -10. What is the type II error rate for this alternative scenario? (c) Compute a 99% confidence interval for the change in mean heart rate mortality. Interpret the interval in context.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![Next, Figure 2 shows a histogram and bar chart of the differences by state in mortality rates
between the two years for the selected states.
0.03-
0.02-
0.01-
0.00-
-
State
Change in heart disease mortality rate (2015 - 2005)
Figure 2: Left, bar chart of change in age-adjusted heart disease mortality rates (deaths per 100,000)
by state between 2005 and 2015; right, histogram of differences by state between the two years.
The differences are calculated as (2015 rate – 2005 rate).
Finally, the summary statistics for the age-adjusted mortality rates in each year separately
(Figure 1) and for the change in rates (Figure 2) are shown below in Table 1.
Mean
Standard deviation
2005
204.00
31.70
2015
162.27
22.29
Change -41.73
14.20
Table 1: Summary statistics (mean and standard deviation) for age-adjusted heart disease mortality
rates in 2005 and 2015, and for the difference in rates for each of the two years.
Change in heart disease mortality rate (2015 - 2005)
density](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8709493-15ec-4bea-8183-026eb1086a68%2F907e4fe3-2e28-45ba-9488-81d87906b06d%2Fb6p58u_processed.png&w=3840&q=75)
Transcribed Image Text:Next, Figure 2 shows a histogram and bar chart of the differences by state in mortality rates
between the two years for the selected states.
0.03-
0.02-
0.01-
0.00-
-
State
Change in heart disease mortality rate (2015 - 2005)
Figure 2: Left, bar chart of change in age-adjusted heart disease mortality rates (deaths per 100,000)
by state between 2005 and 2015; right, histogram of differences by state between the two years.
The differences are calculated as (2015 rate – 2005 rate).
Finally, the summary statistics for the age-adjusted mortality rates in each year separately
(Figure 1) and for the change in rates (Figure 2) are shown below in Table 1.
Mean
Standard deviation
2005
204.00
31.70
2015
162.27
22.29
Change -41.73
14.20
Table 1: Summary statistics (mean and standard deviation) for age-adjusted heart disease mortality
rates in 2005 and 2015, and for the difference in rates for each of the two years.
Change in heart disease mortality rate (2015 - 2005)
density
![• Let X; denote the rate for the ith state in 2005.
• Let Y; denote the rate for the ith state in 2015.
• Let D; = Y; – X; denote the difference in rates for the ith state.
• Let S3, S?, S denote the sample variances and X,Ÿ,D denote the sample means.
• Let 0x,0y denote the nationwide mean mortality rates in 2005 and 2015.
• Let Op = 0y – 0x.
1. Answer the following questions using the differences D1,..., D20 shown in Figure 2.
(a) Test the hypothesis that the mean U.S. mortality rate 0p remained the same or increased
from 2005 to 2015 against the alternative that the mean mortality rate decreased. State
the hypotheses, test statistic, rejection region, and p-value. Interpret the conclusion of
the test at level a = 0.01.
(b) Calculate the power of the test you performed in the previous part at OD = -10. What
is the type II error rate for this alternative scenario?
(c) Compute a 99% confidence interval for the change in mean heart rate mortality. Interpret
the interval in context.
(d) What assumption is being made about the variation in heart disease mortality across
the U.S.? (Consider whether your conclusions are consistent with the possibility that
mortality varies systematically by state as suggested by the CDC comment.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8709493-15ec-4bea-8183-026eb1086a68%2F907e4fe3-2e28-45ba-9488-81d87906b06d%2Fjtks1xu_processed.png&w=3840&q=75)
Transcribed Image Text:• Let X; denote the rate for the ith state in 2005.
• Let Y; denote the rate for the ith state in 2015.
• Let D; = Y; – X; denote the difference in rates for the ith state.
• Let S3, S?, S denote the sample variances and X,Ÿ,D denote the sample means.
• Let 0x,0y denote the nationwide mean mortality rates in 2005 and 2015.
• Let Op = 0y – 0x.
1. Answer the following questions using the differences D1,..., D20 shown in Figure 2.
(a) Test the hypothesis that the mean U.S. mortality rate 0p remained the same or increased
from 2005 to 2015 against the alternative that the mean mortality rate decreased. State
the hypotheses, test statistic, rejection region, and p-value. Interpret the conclusion of
the test at level a = 0.01.
(b) Calculate the power of the test you performed in the previous part at OD = -10. What
is the type II error rate for this alternative scenario?
(c) Compute a 99% confidence interval for the change in mean heart rate mortality. Interpret
the interval in context.
(d) What assumption is being made about the variation in heart disease mortality across
the U.S.? (Consider whether your conclusions are consistent with the possibility that
mortality varies systematically by state as suggested by the CDC comment.)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman