A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees high systolic blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the systolic blood pressure levels of the employees were measured again. Did the program reduce the average systolic blood pressure level? (mud = population mean difference = before - after)

The correct option is (A).

Step-by-step explanation:

The complete question is:

A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees systolic blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the systolic blood pressure levels of the employees were measured again. Did the program reduce the average systolic blood pressure level? Note: Differences were taken by taking "before systolic blood pressure" minus "After blood pressure"

The 95% confidence interval was (5.6, 10.2).

A. On average, the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at the 95% confidence level

B. We are 95% confident that there is no difference in average systolic blood pressure levels before and after the stress reduction program.

C. On average, the systolic blood pressure levels after the stress reduction program were significantly higher than the systolic blood pressure levels before the stress reduction program, at the 95% confidence level.

Solution:

The hypothesis to determine whether the program reduced the average systolic blood pressure level, is as follows:

H₀: The program did not reduced the average systolic blood pressure level, i.e. d = 0.

Hₐ: The program reduced the average systolic blood pressure level, i.e. d ≠ 0.

A 95% confidence interval can be used to make conclusion for a hypothesis test.

If the 95% confidence interval consists of the null value, i.e. 0 then the null hypothesis will not be rejected. And if the confidence interval does not consists of the null value, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the two data is:

(5.6, 10.2)

The 95% confidence interval does not consist of 0, the null value. And since all the values in the 95% confidence interval  are positive it clearly indicates that the program did not reduced the average systolic blood pressure level.

Conclusion:

On average, the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at the 95% confidence level

Thus, the correct option is (A).

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.

answer: the answer is 35%