Questions: Answer the questions using complete sentences. a. An economist noted the correlation between consumer confidence and monthly personal savings was negative. As consumer confidence increases, would monthly personal savings be expected to increase, decrease, or remain constant? b. A study found a correlation between higher education and lower death rates. Does this mean that one can live longer by going to college? Why or why not?

Answer the questions using complete sentences.
a. An economist noted the correlation between consumer confidence and monthly personal savings was negative. As consumer confidence increases, would monthly personal savings be expected to increase, decrease, or remain constant?
b. A study found a correlation between higher education and lower death rates. Does this mean that one can live longer by going to college? Why or why not?

Transcript text: Answer the questions using complete sentences. a. An economist noted the correlation between consumer confidence and monthly personal savings was negative. As consumer confidence increases, would monthly personal savings be expected to increase, decrease, or remain constant? b. A study found a correlation between higher education and lower death rates. Does this mean that one can live longer by going to college? Why or why not?

Solution

Solution Steps

Step 1: Correlation Coefficient Calculation

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Where:

\( \text{Cov}(X,Y) = -2.5 \)
\( \sigma_X = 1.58 \)
\( \sigma_Y = 1.58 \)

Substituting the values, we find:

\[ r = \frac{-2.5}{1.58 \times 1.58} = -1.0 \]

Step 2: Interpretation of Correlation

The correlation coefficient \( r = -1.0 \) indicates a perfect negative correlation between consumer confidence and monthly personal savings. This means that as consumer confidence increases, monthly personal savings are expected to decrease.

Step 3: Answer to Part a

Based on the negative correlation, we conclude:

\[ \text{Monthly personal savings would be expected to decrease, because a negative correlation means that as one variable increases, the other variable tends to decrease.} \]

Step 4: Answer to Part b

The study found a correlation between higher education and lower death rates. However, correlation does not imply causation. While there is an association, it does not mean that attending college directly causes one to live longer. Other factors, such as socioeconomic status, access to healthcare, or lifestyle choices, may contribute to the observed correlation.