Question

describe and correct the error made in classifying the association of the following data table.
the data on the table shows a 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 Option A

In the table, \(x\) values are \(20,19,17,17,15,13,11\) (decreasing from left - to - right). \(y\) values are \(3,6,7,8,10,11,12\) (increasing from left - to - right). Negative association means as \(x\) increases \(y\) decreases or as \(x\) decreases \(y\) increases. Here, as \(x\) decreases \(y\) increases. So, the data shows a negative association.

Step2: Analyze Option B

As \(x\) increases (but in our table \(x\) is decreasing), the statement in Option B is incorrect. The general trend (as \(x\) decreases \(y\) increases) is a negative association, not what Option B claims.

Step3: Analyze Option C

If \(y\) increases from left - to - right and \(x\) decreases from left - to - right (negative association), adjacent \(y\) values: \(6 - 3=3\), \(7 - 6 = 1\), \(8 - 7=1\), \(10 - 8 = 2\), \(11 - 10=1\), \(12 - 11 = 1\). They do not differ by the same amount. But the main point is the association type. Since there is a negative association (from Step 1), Option C is wrong.

Step4: Analyze Option D

The \(x\) value \(17\) occurs twice (\(x = 17\) corresponds to \(y = 7\) and \(y = 8\)). But this is about the association type. The presence of a repeated \(x\) value does not change the fact that there is a negative association (from Step 1). So, Option D is wrong.

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.