Which statement is true?

Question

A strong association implies a positive correlation.
A positive correlation implies a strong association.
A positive correlation implies a positive slope.
A negative correlation implies a weak association.

Answer 1

Let's analyze each statement:

1. A strong association implies a positive correlation. - This statement is not true because a strong association can be either positive or negative.

2. A positive correlation implies a strong association. - This statement is also not necessarily true. A positive correlation indicates a relationship where as one variable increases, the other variable also increases, but it does not indicate the strength of that relationship; it could be weak.

3. A positive correlation implies a positive slope. - This statement is true. A positive correlation means that as one variable increases, the other variable tends to increase as well, which corresponds to a positive slope in a graph.

4. A negative correlation implies a weak association. - This statement is not true, as a negative correlation can be strong or weak. A negative correlation indicates that as one variable increases, the other variable tends to decrease, but the strength of that association can vary.

Based on this analysis, the true statement is:

A positive correlation implies a positive slope.