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	50	49	40	47	45	45	40	41
Left	54	51	41	49	45	48	41	44

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?

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

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

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

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

2. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? ≤ >  αα
5. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, 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 = 0.10, 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 significant at αα = 0.10, 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 = 0.10, 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.

Answer 1

Ans.

Appropriate Test:- t-test for the difference between two dependent population means because the average time to complete an obstacle course is depends on eye.

(a)

Note:- We find test statistics and p-value using R:-

(b). Test Statistics:-

t = -4.321

(c). P-value :-

P-value = 0.0017

(d). P- value = 0.0017 < α = 0.10

(e). Based on this, we reject the null hypothesis.

(f). Final Conclusion:-

The results are statistically significant at α = 0.10, 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.