Question

Is the average time to complete an obstacle course different 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	48	40	40	44	40	47	45	48
Left	45	32	38	43	37	48	43	48

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

The null and alternative hypotheses would be:

The test statistic ? t (3 decimal places)?

The p-value (4 decimal places)?

p value less than or greater than significance level?

reject or fail to reject the null hypothesis?

Thus, the final conclusion is that ...

• 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 not the same as 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 eight volunteers that were completed the course in the same amount of time on average with the patch over the right eye compared to 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 not the same as 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.

Answer 1

(a)

H0: Null Hypothesis: = 0 ( the average time to complete an obstacle course is not different when a patch is placed over the right eye than when a patch is placed over the left eye )

HA: Alternative Hypothesis: 0 ( the average time to complete an obstacle course is different when a patch is placed over the right eye than when a patch is placed over the left eye ) (Claim)

(b)

From the iven data, values of d = Right - Left are got as follows:

d = Right - Left = 3,8,2,1,3,-1,2,0

From d values, the following statistics are calculated:

n = Sample Size = 8

= Mean of d values = 2.25

sd =Standard Deviation of d values = 2.712

Test Statistic is given by:

The test statistic : t = 2.346

(c)

df = 8 - 1 = 7

By Technology:

p - value = 0.0514

(d)

p value is greater than significance level.

(e)

Correct option:

The results are statistically insignificant at α = 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 not the same as the population mean time to complete the obstacle course with a patch over the left eye.