Answer :
Answer
Statement I and statement III are true statements.
Explanation
The question asks us to examine the statements to pick which ones are correct. We are given the scatterplot graph of these two scores, correlation between the midterm and final exam scores, and the corellation coefficient.
y = 90.6 - 0.489x , r = -0.602
The statements to be examined include
I) The same number of students scored 100 on the midterm exam as scored 100 on the final exam.
II) Students who scored higher on the midterm exam tended to score higher on the final exam.
III) The correlation between the midterm and final exam scores is negative.
IV) The standard deviation of the final exam scores is greater than the standard deviation of the midterm exam scores.
So, we then examine the statements one at a time to pick the correct one.
I) The same number of students scored 100 on the midterm exam as scored 100 on the final exam.
From the scatterplot graph, we can see that only 2 students score 100 in the final exam and only 2 students score 100 in the midterm exam too.
This statement is right.
II) Students who scored higher on the midterm exam tended to score higher on the final exam.
Again, from the scatterplot graph, we can see that the students who score high in the midterm exam (two that scored 100, one that scored 90, two out of the three that score 80) all have a corresponding low score (60, 20, 40, 30, 60 respectively) in the final exam.
This statement isn't correct.
III) The correlation between the midterm and final exam scores is negative.
The correlation between the two scores is evident in the value of the correlation coefficient. If it is greater than 0 (that is, a positive number), then there is a positive correlation between the two quantities being compared, but if it is less than 0 (that is, a negative number), there is a negative correlation between the two quantities being compared.
For this question, the correlation coefficient = -0.602 (that is, negative).
Hence, the correlation between the midterm and final exam score is truly negative.
This statement is correct.
IV) The standard deviation of the final exam scores is greater than the standard deviation of the midterm exam scores.
From the scatterplot, we can see that midterm exam scores are more scattered than the final exam score. Hence, the standard deviation of the final exam scores is not greater than the standard deviation of the midterm scores.
This statement is not correct.
Hope this Helps!!!
