Question

describe and correct the error made in describing the association of the following data table.
the data in the table show positive association because y is increasing.
choose the correct answer below.
a. in the table, x decreases from left to right. data with x - values that decrease from left to right on a table show negative association.
b. as x increases, y decreases. this means the data in the table show negative association.
c. in the table, y increases from left to right. however, adjacent y - values do not always differ by the same amount. this means the data in the table show no association.
d. one x - value, 17, occurs twice and corresponds to two different y - values, 7 and 8. this means the data in the table show no association.
e. in the table, y increases from left to right. data with y - values that increase from left to right on a table show negative association.

Explanation:

Step1: Analyze the x - values

The x - values are 19, 18, 17, 17, 15, 13, 11 which are decreasing from left - to - right.

Step2: Analyze the association concept

When x - values decrease from left - to - right and y - values have a certain pattern, we consider the association. In general, when x decreases and y has no clear non - related pattern, a negative association may exist.

Step3: Check each option

• Option A: Correctly states that since x decreases from left to right, data with x - values that decrease from left to right on a table show negative association.
• Option B: x is decreasing not increasing, so this is wrong.
• Option C: Just because adjacent y - values don't differ by the same amount doesn't mean there is no association. There can still be a non - linear association.
• Option D: A repeated x - value with different y - values doesn't necessarily mean no association. There can be a non - one - to - one relationship with an association.
• Option E: y increasing from left to right does not show negative association. Positive association is when y increases as x increases (or y decreases as x decreases in some cases), and negative association is when y decreases as x increases (or y increases as x decreases).

Answer:

A. In the table, x decreases from left to right. Data with x - values that decrease from left to right on a table show negative association.