Victoria, an accomplished marathon runner, claims that the standard deviation for her time to run a 26.2 mile marathon is less than 17.5 minutes. To test her claim, Victoria looks up 11 of her race times (in minutes): 227.2, 233.3, 259.7, 265.8, 252.1, 228.8, 222.6, 202.9, 214.5, 237.2, 267.7 Perform a hypothesis test using a 9% level of significance to test Victoria's claim. Step 1: State the null and alternative hypotheses. Ho:o 2 17.5 Ha:o
Victoria, an accomplished marathon runner, claims that the standard deviation for her time to run a 26.2 mile marathon is less than 17.5 minutes. To test her claim, Victoria looks up 11 of her race times (in minutes): 227.2, 233.3, 259.7, 265.8, 252.1, 228.8, 222.6, 202.9, 214.5, 237.2, 267.7 Perform a hypothesis test using a 9% level of significance to test Victoria's claim. Step 1: State the null and alternative hypotheses. Ho:o 2 17.5 Ha:o
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
Topic Video
Question
![yopenmath.com/assess2/?cid%=101459&aid=7240148#/skip/1
Victoria, an accomplished marathon runner, claims that the standard deviation for her time to run a
26.2 mile marathon is less than 17.5 minutes. To test her claim, Victoria looks up 11 of her race
times (in minutes):
227.2, 233.3, 259.7, 265.8, 252.1, 228.8, 222.6, 202.9, 214.5, 237.2, 267.7
Perform a hypothesis test using a 9% level of significance to test Victoria's claim.
Step 1: State the null and alternative hypotheses.
Ho:0 2v 17.5
H:o<v
17.5
(So we will be performing a left-tailed
V test.)
Part 2 of 4
Step 2: Assuming the null hypothesis is true, determine the features of the distribution of
test statistics.
Because we are testing the population standard deviation, we will use a x
distribution with 10
v degrees of freedom.
Part 3 of 4
Step 3: Find the p-value of the test statistic.
Sample Mean: ¤ =
21.37
Sample Standard Deviation: s =
14.91
P(x 5v 0.09
p-value =
17.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7715250-a16c-4a08-bd4e-10bedd823d58%2Fa132a7ef-1e5b-4580-bd9c-2f2f226e496a%2Fl18xdqyf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:yopenmath.com/assess2/?cid%=101459&aid=7240148#/skip/1
Victoria, an accomplished marathon runner, claims that the standard deviation for her time to run a
26.2 mile marathon is less than 17.5 minutes. To test her claim, Victoria looks up 11 of her race
times (in minutes):
227.2, 233.3, 259.7, 265.8, 252.1, 228.8, 222.6, 202.9, 214.5, 237.2, 267.7
Perform a hypothesis test using a 9% level of significance to test Victoria's claim.
Step 1: State the null and alternative hypotheses.
Ho:0 2v 17.5
H:o<v
17.5
(So we will be performing a left-tailed
V test.)
Part 2 of 4
Step 2: Assuming the null hypothesis is true, determine the features of the distribution of
test statistics.
Because we are testing the population standard deviation, we will use a x
distribution with 10
v degrees of freedom.
Part 3 of 4
Step 3: Find the p-value of the test statistic.
Sample Mean: ¤ =
21.37
Sample Standard Deviation: s =
14.91
P(x 5v 0.09
p-value =
17.5
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.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
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