**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 | 46 | 50 | 42 | 42 | 50 | 47 | 46 | 42 | |-------|----|----|----|----|----|----|----|----| | Left | 45 | 48 | 41 | 41 | 48 | 45 | 46 | 43 | Assume a Normal distribution. What can be concluded at the α = 0.10 level of significance? For this study, we should use [Select an answer]. **a. The null and alternative hypotheses would be:** - \( H_0 \): [Select an answer] [Select an answer] (please enter a decimal) - \( H_1 \): [Select an answer] [Select an answer] (Please enter a decimal) **b. The test statistic \( = \) [Enter value] (please show your answer to 3 decimal places.)** **c. The P-value \( = \) [Enter value] (Please show your answer to 4 decimal places.)** **d. The P-value is [Select an answer] α** **e. Based on this, we should [Select an answer] the null hypothesis.** **f. Thus, the final conclusion is that ...** - ○ The results are statistically insignificant at \( \alpha = 0.10 \), 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 significant at \( \alpha = 0.10 \), so there is sufficient evidence to conclude that... [Complete the statement].
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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![**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 | 46 | 50 | 42 | 42 | 50 | 47 | 46 | 42 |
|-------|----|----|----|----|----|----|----|----|
| Left | 45 | 48 | 41 | 41 | 48 | 45 | 46 | 43 |
Assume a Normal distribution. What can be concluded at the α = 0.10 level of significance?
For this study, we should use [Select an answer].
**a. The null and alternative hypotheses would be:**
- \( H_0 \): [Select an answer] [Select an answer] (please enter a decimal)
- \( H_1 \): [Select an answer] [Select an answer] (Please enter a decimal)
**b. The test statistic \( = \) [Enter value] (please show your answer to 3 decimal places.)**
**c. The P-value \( = \) [Enter value] (Please show your answer to 4 decimal places.)**
**d. The P-value is [Select an answer] α**
**e. Based on this, we should [Select an answer] the null hypothesis.**
**f. Thus, the final conclusion is that ...**
- ○ The results are statistically insignificant at \( \alpha = 0.10 \), 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 significant at \( \alpha = 0.10 \), so there is sufficient evidence to conclude that... [Complete the statement].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F394c1108-2c1d-4d7b-8393-07c0a528de65%2F02309bb1-e7c1-4daf-958c-910d0401efab%2F6xh1flw_processed.png&w=3840&q=75)
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