A company which designs sports shoes has made an improvement to their popular running shoe. they hope that athletes wearing the new running shoe will be able to run faster over short distances. they will use a paired sample to determine whether the mean time to run 100 meters for sprinters wearing the new running shoe is less than the mean time to run the 100 meters for sprinters wearing the old running shoe. identify the variable for the proposed hypothesis test.

Independent variable = new running shoe

Dependent variable = mean time

Step-by-step explanation:

Remember, that every statistical research method employs the use of variables (properties) of things which can change in value.

Therefore, matching the variable to proposed hypothesis test could be rendered as:

"To determine whether there is a statistically significant impact of wearing the new running shoe on the mean time to run 100 meters by sprinters."

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.