Is the average time to complete an obstacle course shorter when a patch is placed over the right eye than when a patch is placed over the left eye? Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. "Left" means the patch was placed over the left eye and "Right" means the patch was placed over the right eye. Time to Complete the Course Right 49 50 48 41 49 44 49 41 Left 48 54 54 42 50 46 47 40 Assume a Normal distribution.  What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use Select an answer t-test for the difference between two independent population means? z-test for a population proportion? z-test for the difference between two population proportions t-test for the difference between two dependent population means t-test for a population mean  The null and alternative hypotheses would be:              H0: Select an answer μ1,  μd, or  p1  Select an answer = ≠ > <  Select an answer 0 ,  μ2, or  p2  (please enter a decimal)     H1:H1:  Select an answer μd, μ1, or p1  Select an answer < ≠ > =  Select an answer p2 , μ2, or  0  (Please enter a decimal)           2. The test statistic ? z  or t  = ______ (please show your answer to 3 decimal places.)           The p-value =______  (Please show your answer to 4 decimal places.)            The p-value is ? ≤ or  >  α         3. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.  Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye.  The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the eight volunteers that were completed the course faster on average with the patch over the right eye compared to the left eye. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye.

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
Topic Video
Question

Is the average time to complete an obstacle course shorter when a patch is placed over the right eye than when a patch is placed over the left eye? Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. "Left" means the patch was placed over the left eye and "Right" means the patch was placed over the right eye.

Time to Complete the Course

Right 49 50 48 41 49 44 49 41
Left 48 54 54 42 50 46 47 40

Assume a Normal distribution.  What can be concluded at the the αα = 0.05 level of significance level of significance?

For this study, we should use Select an answer t-test for the difference between two independent population means? z-test for a population proportion? z-test for the difference between two population proportions t-test for the difference between two dependent population means t-test for a population mean 

  1. The null and alternative hypotheses would be:   
  2.   

       H0: Select an answer μ1,  μd, or  p1  Select an answer = ≠ > <  Select an answer 0 ,  μ2, or  p2  (please enter a decimal)   

 H1:H1:  Select an answer μd, μ1, or p1  Select an answer < ≠ > =  Select an answer p2 , μ2, or  0  (Please enter a decimal)

          2. The test statistic ? z  or t  = ______ (please show your answer to 3 decimal places.)

          The p-value =______  (Please show your answer to 4 decimal places.)

           The p-value is ? ≤ or  >  α

        3. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.

 Thus, the final conclusion is that ...

  • The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye. 
  • The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye.
  • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the eight volunteers that were completed the course faster on average with the patch over the right eye compared to the left eye.
  • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
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