QuestionTwenty different statistics students are randomly selected. For each of them, their body temperature is measured and their head circumference is measured. If it is found that , does that indicate that there is no association between these two variables?
Choose the correct answer below.
A. No, because if , the variables are in a perfect linear relationship.
B. No, because r does not measure the strength of the relationship, only its direction.
C. No, because while there is no linear correlation, there may be a relationship that is not linear.
D. Yes, because if , the variables are completely unrelated.
Studdy Solution
STEP 1
1. The correlation coefficient is calculated between body temperature and head circumference.
2. indicates no linear correlation.
STEP 2
1. Understand the meaning of the correlation coefficient .
2. Evaluate the implications of .
3. Choose the correct answer based on the implications.
STEP 3
The correlation coefficient measures the strength and direction of a linear relationship between two variables.
STEP 4
If , it indicates that there is no linear correlation between the two variables. However, this does not imply that there is no relationship at all; there may be a non-linear relationship.
STEP 5
Based on the implications of , the correct answer is:
C. No, because while there is no linear correlation, there may be a relationship that is not linear.
The correct answer is:
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