A statistics professor randomly selects 31 students from their morning class and asks ``How much sleep did youget the night before?''. The sample average was 6.5 hours, and the sample standard deviation was 3.2 hours. a) Find the 95% confidence interval for the average sleep (in hours) that statistics students in the morning class gotthe night before and interpret your interval in terms of the problem.

The 95% confidence interval for the average sleep (in hours) that statistics students in the morning class got the night before is between 5.37 hours and 7.63 hours. This means that we are 95% that the true mean sleep that all statistics students in the morning class got the night before is between 5.37 hours and 7.63 hours.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the mean subtracted by M. So it is 6.5 - 1.13 = 5.37 hours

The upper end of the interval is the mean added to M. So it is 6.5 + 1.13 = 7.63 hours

The 95% confidence interval for the average sleep (in hours) that statistics students in the morning class got the night before is between 5.37 hours and 7.63 hours. This means that we are 95% that the true mean sleep that all statistics students in the morning class got the night before is between 5.37 hours and 7.63 hours.

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: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: