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. Is the average time to complete an obstacle course different when a patch is placed over the right eye than when apatch is placed over the left eye? Thirteen randomly selected volunteers first completed an obstacle course with apatch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. Thecompletion times are shown below. "Left" means the patch was placed over the left eye and "Right" means thepatch was placed over the right eye.Time to Complete the CourseRight 48 42 49 50 44 45 45 42Left 50 40 46 49 43 44 41 40Assume a Normal distribution. What can be concluded at the the a = 0.05 level of significance level ofsignificance?For this study, we should use Select an answera. The null and alternative hypotheses would be:Ho: Select an answer ? Select an answer (please enter a decimal)H1: Select an answer? Select an answer (Please enter a decimal)b. The test statistic ?c. The p-value =d. The p-value is ? ae. Based on this, we should Select an answer the null hypothesis.(please show your answer to 3 decimal places.)| (Please show your answer to 4 decimal places.) f. Thus, the final conclusion is that .The results are statistically insignificant at a = 0.05, so there is statistically significant evidence toconclude that the population mean time to complete the obstacle course with a patch over the right eyeis equal to the population mean time to complete the obstacle course with a patch over the left eye.The results are statistically significant at a = 0.05, so there is sufficient evidence to conclude that theeight volunteers that were completed the course in the same amount of time on average with the patchover the right eye compared to the left eye.The results are statistically insignificant at a = 0.05, so there is insufficient evidence to conclude thatthe population mean time to complete the obstacle course with a patch over the right eye is not thesame as the population mean time to complete the obstacle course with a patch over the left eye.The results are statistically significant at a = 0.05, so there is sufficient evidence to conclude that thepopulation mean time to complete the obstacle course with a patch over the right eye is not the sameas the population mean time to complete the obstacle course with a patch over the left eye.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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.

f. Thus, the final conclusion is that .
The results are statistically insignificant at a = 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 significant at a = 0.05, 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 insignificant at a = 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 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 a = 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 not the same
as the population mean time to complete the obstacle course with a patch over the left eye.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

For the given data on course completion time with patches for right and left eyes, since the same volunteers are used for both the courses, a paired t-test for difference of means will be used to test whether there is any difference between the two samples.

Let the difference between the two sample values be denoted by:

$d_{i} = r_{i} - l_{i} i = 1, 2 . . 8$

Level of significance is: $α = 0.05$

The hypothesis to be tested are:

$H_{0} : μ_{d} = 0 H_{1} : μ_{d} \neq 0 w h e r e μ_{d} i s t h e p o p u l a t i o n m e a n d i f f e r e n c e$

Using Excel to perform the test:

Input the data in spreadsheet
Go to Data tab > Data Analysis > t-test: Paired two sample for means
Input the range for the two variables, and level of significance = 0.05 > Click OK

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