A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 30 tires surveyed, the mean lifespan was 46,300 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? 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 (a)         Part (b)         Part (c)         Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X  ~      ,     Part (e) 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.)      =  Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If  H0  is true, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.If  H0  is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.    If  H0  is false, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.If  H0  is false, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less. Correct! A p-value is the probability that an outcome of the data will happen purely by chance when  H0  is true. Part (g)         Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? =  (ii) Decision: reject the null hypothesisdo not reject the null hypothesis     (iii) Reason for decision: Since ? < p-value, we do not reject the null hypothesis.Since ? > p-value, we do not reject the null hypothesis.    Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the average life span of the tires is less than 50,000.There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 30 tires surveyed, the mean lifespan was 46,300 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?

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 (a)

     
     
     
     
  • Part (b)

     
     
     
     
  • Part (c)

     
     
     
     
  • Part (d)

    State the distribution to use for the test. (Round your answers to two decimal places.)
    X
     ~  
     
      ,  
     
  • Part (e)

    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.)
         = 
  • Part (f)

    What is the p-value? (Round your answer to four decimal places.)


    Explain what the p-value means for this problem.
    If 
    H0
     is true, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.If 
    H0
     is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.    If 
    H0
     is false, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.If 
    H0
     is false, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.
    Correct! A p-value is the probability that an outcome of the data will happen purely by chance when 
    H0
     is true.
  • Part (g)

       
       
  • Part (h)

    Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
    (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
    ? = 

    (ii) Decision:
    reject the null hypothesisdo not reject the null hypothesis    

    (iii) Reason for decision:
    Since ? < p-value, we do not reject the null hypothesis.Since ? > p-value, we do not reject the null hypothesis.    Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis.

    (iv) Conclusion:
    There is sufficient evidence to conclude that the average life span of the tires is less than 50,000.There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.    
  • Part (i)

    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 bounds to the nearest whole number.)
     
 

Additional Materials

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
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
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman