Six people participate in a coordination study. They are each timed (in seconds) for how long they can jump rope without a mistake with their eyes open. Then, they each repeat the task with their eyes closed. For each individual, the difference in times is calculated. The purpose of the study is to determine if the lack of vision in normally seeing individuals decreases (hint for Steps 2, 4, & 6) coordination.

a. )Select the appropriate test and justify your decision.

The paired t-test is an appropriate test for this test to determine if the lack of vision in normally seeing individuals decreases coordination.

Step-by-step explanation:

Since the data that will be provided for eyes opened and eyes closed are for the same individuals, it's no brainer that one of the most appropriate hypothesis test for this data described is the paired t-test.

The null and the alternative hypothesis are first postulated.

Since the major aim of the study is to check if the lack of vision decreases coordination, the null hypothesis would be that the lack of vision in normally seeing individuals increases or has no effect on coordination and the participants would spend more or equal time jumping the ropes without mistakes when their eyes are closed than when their eyes are opened.

The alternative hypothesis has to confirm the initial test hypothesis that the lack of vision in normally seeing individuals decreases coordination and the participants would spend less time jumping the ropes without mistakes when their eyes are closed than when their eyes are opened.

If the time taken to jump the ropes without mistakes with eyes are open is t₁

And the time taken to jump the ropes without mistakes when the eyes are closed is t₂

If the difference between the two of them is termed μ₀

μ₀ = t₂ - t₁

The null hypothesis can be stated mathematically as

H₀: t₂ ≥ t₁

Or

H₀: μ₀ ≥ 0

And the alternative hypothesis would be

Hₐ: t₂ < t₁

Or

Hₐ: μ₀ < 0

The p-value is then calculated and interpreted as thus,

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, this explains an appropriate test and how to go about it.

Hope this Helps!!!

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is