Question

In a German study from the 1930s, the population of a large town is compared to the size of the local flocks of storks. The study stated a linear correlation coefficient of 0.97. Which of the following is a correct interpretation of this value?

a. These two variables show strong positive correlation. An increase in the number of storks in the area is related to a statistically significant increase in the population in the town.

b. These two variables show weak positive correlation. An increase in the number of storks in the area is related to an increase in the population of the town, but the increase is not statistically significant.

c. These two variables show strong negative correlation. An increase in the number of storks in the area is related to a statistically significant decrease in the population of the town.

d. These two variables show weak negative correlation. An increase in the number of storks in the area is related to a decrease in the population of the town, but the decrease is not statistically significant. 10 points QUESTION 2

Answer 1

Solution:

Given:  a linear correlation coefficient between the number of storks in the area and the population in the town is 0.97.

that is: r = 0.97

Following are the interpretations are for correlation coefficient r :

1) If r = -1 , then there is perfect negative correlation
2) if -1 < r ≤ 0.80 , then there is Strong negative correlation
3) if -0.80 < r ≤ -0.30, then there is moderate negative correation
4) if -0.30 < r < 0 , then there weak negative correlation
5) if r = 0 , then there no or zero correlation
6) if 0 < r < 0.30 then there is weak positive correlation
7) if 0.30 ≤ r < 0.80 , then there is moderate positive correlation
8) if 0.80 ≤ r < 1 , then there is strong positive correlation
9) if r = 1 , then there is perfect positive correlation

Since r = 0.97 is between 0.80 and 1, thus there is strong positive correlation.

thus correct answer is:

a. These two variables show strong positive correlation. An increase in the number of storks in the area is related to a statistically significant increase in the population in the town.