Question

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? 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	48	49	50	42	40	42	48
Left	50	46	49	47	42	41	42	49

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

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

1. The null and alternative hypotheses would be:

H0: μd, μ1, p1? > ≠ < =? μ2 p2 0? (please enter a decimal)   

H1: p1, μd, μ1? = < > ≠? μ2, p2, 0  (Please enter a decimal)

2. The test statistic t or z  = ____ (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? > or ≤  α
5. Based on this, we should: reject, accept, fail to reject  the null hypothesis.
6. Thus, the final conclusion is that ...
   • 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 greater than the population mean time to complete the obstacle course with a patch over the left eye.
   • The results are statistically insignificant at αα = 0.10, 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.
   • 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 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 = 0.10, 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.

Answer 1

For this study, we should use: t-test for the difference between two dependent population means

1. The null and alternative hypotheses would be:

H0: μd = 0  

H1: μd > 0  

1. The test statistic t = 0.753
2. The p-value = 0.2379
3. The p-value is > α
4. Based on this, we should: fail to reject  the null hypothesis.
5. 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 greater than the population mean time to complete the obstacle course with a patch over the left eye.