Suppose that you are asked to conduct a study to determine whether smaller class
sizes lead to improved student performance of fourth graders.
a. if you could conduct any experiment you want, what would you do? be
specific.
b. more realistically, suppose you can collect observational data on several
thousand fourth graders in a given state. you can obtain the size of their
fourth grade class and a standardized test score taken at the end of fourth
grade. why might you expect a negative correlation between class size
and test score?
c. would a negative correlation necessarily show that a smaller class size
cause better performance? explain.

a. correlation

b. inverse linear correlation exists If the higher the population of students lead to a decrease in test score,

c. yes

Step-by-step explanation:

a. Correlation is a measure of the amount of association existing between two variables.

b. For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists,

Similarly,when a straight line having a negative gradient can reasonably be drawn through points on a graph, negative or inverse linear correlation exists,

The results of this determination give values of r lying between +1 and −1, where +1 indicates perfect direct  Positive linear correlation and −1 indicates perfect inverse correlation or Negative linear correlation and 0 indicates that no correlation exists.

If the higher the population of students lead to a decrease in test score, there will definitely be a negative correlation between class size and test score. i.e low class size result in high test score which consequently lead to high performance.

c. YES

A negative correlation means low class size result in high test score which consequently lead to better performance.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

x=30

step-by-step explanation: