Descriptions of three studies are given. In each of the studies, the two populations of interest are students majoring in science at a particular university and students majoring in liberal arts at this university. For each of these studies, indicate whether the samples are independently selected or paired. Study 1: To determine if there is evidence that the mean number of hours spent studying per week differs for the two populations, a random sample of 100 science majors and a random sample of 75 liberal arts majors are selected. independently selected paired Study 2: To determine if the mean amount of money spent on textbooks differs per semester, a random sample of science majors is selected. Each student in this sample is asked for two data values: how much money they spent on textbooks in the spring semester and how much money they spent on textbooks in the fall semester. independently selected paired Study 3: To determine if the mean amount of time spent using the campus library differs for the two populations, a random sample of science majors is selected. A separate random sample of the same size is selected from the population of liberal arts majors. independently selected paired

Independently sample data measure the very same factor but for two separate groups of instances, whereas paired-samples test the same factor but for the same selection of studies.

For point 1:

For point 2:

For point 3:

Therefore, the final answer is "Independently selected, paired, and Independently selected ".

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Step-by-step explanation:

Independently selected samples measures scores on the same variable but for two different groups of cases while Paired-samples measures scores on two different variables but for the same group of cases.

In case study 1, the sample is independently selected; a random sample of 100 science majors and a random sample of 75 liberal arts majors are selected: two different group of cases and just one variable, to compare the mean number of hours.

In case study 2, the samples are paired, a random sample of science majors is selected. Each student in this sample is asked for two data values: a group of case but two different variables; how much money they spent on textbooks in the spring semester and how much money they spent on textbooks in the fall semester were measured.

In case study 3, the samples were independently selected. Two different group of cases; a random sample of science majors is selected. A separate random sample of the same size is selected from the population of liberal arts majors were measured for just one variable the mean amount of time spend in campus.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.