Is the average time to complete an obstacle course longer when a patch is placed over the right eye than when a patch is placed over the left eye? Eight 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. Right 40 46 42 45 40 48 42 42 Left 38 46 41 45 36 45 39 43 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        The null and alternative hypotheses would be:        H0:H0:                  (please enter a decimal)     Ha:Ha:                  (Please enter a decimal) The test statistic     =  (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      the null hypothesis. Thus, the final conclusion is that ... 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 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 greater than the population mean time to complete the obstacle course with a patch over the left eye. The results are statistically significant at αα = 0.05, 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 greater than the population mean time to complete the obstacle course with a patch over the left eye. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the eight volunteers that were completed the course slower on average with the patch over the right eye compared to the left eye.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Is the average time to complete an obstacle course longer when a patch is placed over the right eye than when a patch is placed over the left eye? Eight 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.

Right 40 46 42 45 40 48 42 42
Left 38 46 41 45 36 45 39 43

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       

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

 H0:H0:                  (please enter a decimal)   

 Ha:Ha:                  (Please enter a decimal)

  1. The test statistic     =  (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      the null hypothesis.
  5. Thus, the final conclusion is that ...
    • 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 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 greater than the population mean time to complete the obstacle course with a patch over the left eye.
    • The results are statistically significant at αα = 0.05, 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 greater than the population mean time to complete the obstacle course with a patch over the left eye.
    • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the eight volunteers that were completed the course slower on average with the patch over the right eye compared to the left eye.
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