Questions: A statistics professor warns her class that her second midterm is always harder than the first. She tells her class that students always score 10 points worse on the second midterm compared to their score on the first midterm. This means that the correlation between students' scores on the first and second exam is (a) 1 . (b) -1 . (c) Can't tell without seeing the data.

A statistics professor warns her class that her second midterm is always harder than the first. She tells her class that students always score 10 points worse on the second midterm compared to their score on the first midterm. This means that the correlation between students' scores on the first and second exam is
(a) 1 .
(b) -1 .
(c) Can't tell without seeing the data.

Transcript text: A statistics professor warns her class that her second midterm is always harder than the first. She tells her class that students always score 10 points worse on the second midterm compared to their score on the first midterm. This means that the correlation between students' scores on the first and second exam is (a) 1 . (b) -1 . (c) Can't tell without seeing the data.

Solution

Solution Steps

Step 1: Understanding the Problem

The problem states that students score 10 points worse on the second midterm compared to the first. We need to determine the correlation between the scores on the first and second exams.

Step 2: Analyzing the Relationship

The relationship described is a perfect linear relationship where the score on the second exam is always 10 points less than the score on the first exam. This can be expressed as:

\[ y = x - 10 \]

where \( y \) is the score on the second exam and \( x \) is the score on the first exam.

Step 3: Determining the Correlation

The correlation coefficient measures the strength and direction of a linear relationship between two variables. In this case, since the relationship is perfectly linear and negative (as the second score decreases by a constant amount relative to the first), the correlation is -1.

Final Answer

The answer is \(\boxed{-1}\).

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