Question

In: Statistics and Probability

Is the average time to complete an obstacle course shorter when a patch is placed over...

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)

  1. The test statistic ? z t  =  (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 Select an answer fail to reject accept 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 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.

Solutions

Expert Solution

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.


Related Solutions

Is the average time to complete an obstacle course shorter when a patch is placed over...
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...
Is the average time to complete an obstacle course different when a patch is placed over...
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...
Is the average time to complete an obstacle course different when a patch is placed over...
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...
a) A stock has traded at an average price of $50 over the course of a...
a) A stock has traded at an average price of $50 over the course of a trading day. The covariance of successive transaction price changes (trade-by-trade changes in price) is about -0.06. Using the Roll model, what is the estimate of the bid-ask spread of the stock (measured in percent of the average price of $50)? b) The market index has average return 7% and standard deviation 30%. The risk-free rate is 3%. A portfolio has beta 1.4, unsystematic variance...
The time needed to complete a final t3st in a particular college course used to be...
The time needed to complete a final t3st in a particular college course used to be with a mean of 80 minutes and a standard deviation of 10 minutes. a. What is the probability of completing the 3xam in one hour or less? b. What is the probability that a student will complete the 3xam in more than 60 minutes but less than 75 minutes?
Assume that the time needed to complete a midterm exam for a particular course is normally...
Assume that the time needed to complete a midterm exam for a particular course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes. 5- What percentage of the class is expected to complete the exam within 60 minutes? 6- What percentage of the class is predicted to NOT complete the exam within 115 minutes? 7- If the time limit is 100 minutes and there are 200 students in the class, how many of...
It is time to decide on the software project that you will plan over the span of this course.
An expense tracker (Software Project)It is time to decide on the software project that you will plan over the span of this course. This planning will consist of broad overview as well as some detailed-level aspects over the term. In this first installment of the project you just need to describe the project. Use the following questions to assist you in describing your software system:1. What is the title of your software system?2. What purpose will the software serve?3. Who...
The time needed to complete a final examination in a particular college course is normally distributed...
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 83 minutes and a standard deviation of 13 minutes. Answer the following questions. a. What is the probability of completing the exam in one hour or less (to 4 decimals)? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? c. Assume that the class...
The time needed to complete a final examination in a particular college course is normally distributed...
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 83 minutes and a standard deviation of 13 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places. Use Table 1 in Appendix B. What is the probability of completing the exam in one hour or less (to 4 decimals)? What is the probability that a student will complete the exam in more than...
1. The time need to complete a final examination in a college course is normally distributed...
1. The time need to complete a final examination in a college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. a. What is the probability of completing the exam in less than 60 minutes? b. What is the probability of completing the exam in less than 95 minutes? c. What is the probability of completing the exam in more than 75 minutes? d. What is the probability of completing the exam...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT