Math 110 Module 9 Exam
Exam Page 1
Suppose you have 45 data points and you calculate the sample correlation coefficient and find that r
= .32. Can you be 95% confident that a linear relation exists between the variables? If so, is the
relation positive or negative? Justify you answer.
n = 45
r = .32 = |.32|
critical value = 0.2944
the absolute value is more than the critical value, there is a positive linear relationship.
-1.0 points
Instructor Comments
You can see the correct critical value in the Answer Key.
Answer Key
Suppose you have 45 data points and you calculate the sample correlation coefficient and find that r
= .32.Can you be 95% confident that a linear relation exists between the variables? If so, is the
relation positive or negative? Justify you answer.
Note that for n=45 and 95% we get a value from the chart of .29396. The absolute of r is |r|=.32,
which is above .29396. So a positive linear relation exists.
Exam Page 2
Suppose you have 34 data points and you calculate the sample correlation coefficient and find that r
= - .35. Can you be 95% confident that a linear relation exists between the variables? If so, is the
relation positive or negative? Justify you answer.
n = 24
r = -.35 = |.35|
critical value = 0.33879
, since the absolute value of r is negative and is lighter than the critical value, we can be 95% positive
that there is a negative linear relationship.
Instructor Comments
Very good.
Answer Key
Suppose you have 34 data points and you calculate the sample correlation coefficient and find that r
= - .35. Can you be 95% confident that a linear relation exists between the variables? If so, is the
relation positive or negative? Justify you answer.
Note that for n=34 and 95% we get a value from the chart of .33879. The absolute of r is |r|=.35,
which is above .33879. So a negative linear relation exists.
Exam Page 3
Compute the sample correlation coefficient for the following data:
Can you be 95% confident that a linear relation exists between the variables? If so, is the relation
positive or negative? Justify you answer.
n=5
r = .99
critical value = .87834
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