The null and alternative hypotheses would be:        H0:H0:  Select an answer p1 μ1 μd  Select an answer > ≠ = <  Select an answer 0 μ2 p2  (please enter a decimal)     H1:H1:  Select an answer μ1 p1 μd  Select an answer ≠ = > <  Select an answer μ2 p2 0  (Please enter a decimal) The test statistic ? z t  =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is ? > ≤  αα Based on this, we should Select an answer reject accept fail to reject  the null hypothesis. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.01, 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 insignificant at αα = 0.01, 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 significant at αα = 0.01, 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. The results are statistically insignificant at αα = 0.01, 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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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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 40 40 45 41 43 42 43 43
Left 39 44 45 41 44 42 45 43

Assume a Normal distribution.  What can be concluded at the the αα = 0.01 level of significance level of significance?

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

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

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

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

  1. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The results are statistically significant at αα = 0.01, 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 insignificant at αα = 0.01, 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 significant at αα = 0.01, 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.
    • The results are statistically insignificant at αα = 0.01, 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.
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