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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 | 44 | 40 | 45 | 45 | 40 | 44 | 48 | 44 |
|---|---|---|---|---|---|---|---|---|
| Left | 43 | 38 | 44 | 45 | 40 | 43 | 49 | 42 |
Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance?
For this study, we should use
- The null and alternative hypotheses would be:
H0:H0: (please enter a decimal)
H1:H1: (Please enter a decimal)
- The test statistic = (please show your answer to 3 decimal places.)
- The p-value = (Please show your answer to 4 decimal places.)
- The p-value is αα
- Based on this, we should the null hypothesis.
- Thus, the final conclusion is that ...
- The results are statistically significant at αα = 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 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 = 0.05, 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.
- The results are statistically insignificant at αα = 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 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 = 0.05, 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.
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