MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
![### Understanding Variability in Cross-Country Running Splits
In college, talented runners may join a cross-country team. Runners tend to run their best times when they run even splits. Even splits occur when the runners maintain an even pace throughout the race.
The cross-country coach wants to estimate the typical variability in his best runner's 1-mile splits. He takes a random sample of 25 of this runner's mile splits and finds that this runner's mean 1-mile split is 5.44 minutes per mile, with a standard deviation of 0.14 minutes per mile. This runner's 1-mile splits follow a normal distribution.
#### Task (a):
Find the chi-square critical values \( \chi_L^2 \) and \( \chi_U^2 \) to be used in constructing a 95% confidence interval for the true population standard deviation. (Round your answers to two decimal places.)
\[ \chi_L^2 = \_\_\_\_\_\_ \]
\[ \chi_U^2 = \_\_\_\_\_\_ \]
#### Task (b):
Find the 95% confidence interval for the true variability in his best runner's 1-mile splits. (Round your answers to three decimal places.)
- Lower bound: \_\_\_\_\_\_
- Upper bound: \_\_\_\_\_\_
This problem involves understanding the role of variability and standard deviation in measuring performance consistency. By analyzing the data through chi-square critical values and confidence intervals, we can make informed estimates about true performance variability.](https://content.bartleby.com/qna-images/question/9870bfeb-e26e-42f8-8342-bb7dac6347ce/f1342f13-27fa-4eb3-9f1a-a61a6f9ffe22/c8uyiwu_processed.jpeg)
Transcribed Image Text:### Understanding Variability in Cross-Country Running Splits
In college, talented runners may join a cross-country team. Runners tend to run their best times when they run even splits. Even splits occur when the runners maintain an even pace throughout the race.
The cross-country coach wants to estimate the typical variability in his best runner's 1-mile splits. He takes a random sample of 25 of this runner's mile splits and finds that this runner's mean 1-mile split is 5.44 minutes per mile, with a standard deviation of 0.14 minutes per mile. This runner's 1-mile splits follow a normal distribution.
#### Task (a):
Find the chi-square critical values \( \chi_L^2 \) and \( \chi_U^2 \) to be used in constructing a 95% confidence interval for the true population standard deviation. (Round your answers to two decimal places.)
\[ \chi_L^2 = \_\_\_\_\_\_ \]
\[ \chi_U^2 = \_\_\_\_\_\_ \]
#### Task (b):
Find the 95% confidence interval for the true variability in his best runner's 1-mile splits. (Round your answers to three decimal places.)
- Lower bound: \_\_\_\_\_\_
- Upper bound: \_\_\_\_\_\_
This problem involves understanding the role of variability and standard deviation in measuring performance consistency. By analyzing the data through chi-square critical values and confidence intervals, we can make informed estimates about true performance variability.
Expert Solution
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 nowThis is a popular solution!
Step by stepSolved in 4 steps with 3 images
Knowledge Booster
Similar questions
- In 1940 the average size of a U.S. farm was 174 acres. Let's say that the standard deviation was 58 acres. Suppose we randomly survey 41 farmers from 1940. The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between what two values? (Round your answers to two decimal places.)arrow_forwardFrom generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 41 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value Part 2) Alpha (Enter an exact number as an integer, fraction, or decimal.)α = Part 3) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper…arrow_forwardFrom generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 42 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test. (Round your answers to four decimal places.) X ~ , What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) = What is the p-value? (Round your answer to four decimal places.)arrow_forward
- One of the z-score formulas will help on this question. Scores on the SAT test are normally distributed with a mean of 500 and standard deviation of 100 points. Pretend someone scored 400 on the math portion of the SAT test. What would be the z-score cut off for this score? A. 1.0 B. -1.0 C. 0 D. 2.0arrow_forwardA population has a standard deviation ? of 25 units. (Give your answers correct to two decimal places.) (a) Find the standard error for the mean if n = 30.(b) Find the standard error for the mean if n = 46.(c) Find the standard error for the mean if n = 71.arrow_forwardA queueing system has an arrival rate of 37 visitors per day (standard deviation of 32) and a service rate of 42 visitors per day (standard deviation of 25). (Round your answer to three decimal places.) What is the coefficient of variation of the arrival rate?arrow_forward
- Exercise 6. Regression Fallacy. Historically, scores on the two midterms had a correlation of 0.48. Suppose that Jeri scored 2.1 standard deviations below the mean on the first midterm. (a) How many standard deviations [above or below?] the mean would you predict for her second midterm?arrow_forwardA standardized exam's scores are normally distributed. In a recent year, the mean test score was 1511 and the standard deviation was 312. The test scores of four students selected at random are 1910, 1280, 2240, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1910 is (Round to two decimal places as needed.) The z-score for 1280 is (Round to two decimal places as needed.) The Z-score for 2240 is (Round to two decimal places as needed.) The Z-score for 1420 is (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice OA. The unusual value(s) is/are (Use a comma to separate answers as needed.) OB. None of the values are unusual.arrow_forwardA standardized exam's scores are normally distributed. In a recent year, the mean test score was 1522 and the standard deviation was 311. The test scores of four students selected at random are 1950, 1260, 2190, and 1410. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1950 is. (Round to two decimal places as needed.)arrow_forward
- You determine that the standard deviation for a sample of test scores is 0. This tells you that 1 all the test scores must be 0. 2 all the test scores must be the same value. 3 there is no straight-line association. 4 the mean test score must also be 0. 5 you made a mistake because the standard deviation can never be 0.arrow_forwardA standardized test is given to a sixth-grade class. Historically the mean score has been 151 with a standard deviation of 21. The superintendent believes that the standard deviation of performance may have recently decreased. She randomly sampled 23 students and found a mean of 161 with a standard deviation of 18.2898. Is there evidence that the standard deviation has decreased at the α=0.05 level? Step 1 of 5 : State of the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. Step 3 of 5 : Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5 : Make the decision. Step 5 of 5 : What is the conclusion?arrow_forwardStudent Satisfaction sent from average to the 60th percentile (z score = .2533). Dr. Reed wants to know the projected impact on test scores. All she knows is that Student Satisfaction and Student Test scores are correlated at .43 and the current average test score is 81% with a standard deviation of 5%. Show your workarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
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...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
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
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman