Question

juniors and seniors were surveyed about whether they plan to attend a school dance.

• 94 out of 130 juniors plan to attend.
• 12 out of 140 seniors do not plan to attend.

the following table shows the results.
what mistake was made in the table?
a. the total for the number of seniors is incorrect.
b. the responses for the seniors are reversed.
c. the responses for the juniors are reversed.
d. the number of juniors not attending is incorrect.

Explanation:

Step1: Calculate the correct total for seniors

The number of seniors who plan to attend is \(12\), and the number of seniors who do not plan to attend is \(128\). So the total number of seniors should be \(12 + 128=140\), which is correct as per the table.

Step2: Calculate the correct total for juniors

The number of juniors who plan to attend is \(94\), and the number of juniors who do not plan to attend is \(36\). So the total number of juniors should be \(94 + 36 = 130\), which is correct as per the table.

Step3: Check the totals for "Yes" and "No"

For "Yes" (attending), the total should be \(12+94 = 106\) (correct). For "No" (not - attending), the total should be \(128 + 36=164\) (correct).

Step4: Analyze the reversal

The values for seniors (\(12\) and \(128\)) and juniors (\(94\) and \(36\)) are not reversed. But if we look at the "Total" row for "Yes" and "No": The response for seniors (\(12\) in "Yes" and \(128\) in "No") and for juniors (\(94\) in "Yes" and \(36\) in "No") are not reversed. However, if we consider the columns, the problem is that the responses for seniors and juniors are in the wrong columns. The values for seniors should be in the "Seniors" column and for juniors in the "Juniors" column. But here, it's as if the counts for seniors and juniors are reversed in the sense that the non - attending count for juniors (\(36\)) and attending count for juniors (\(94\)) are correct, but if we assume a wrong - column placement (mentally swapping the idea of which column represents which grade), we can see:
The mistake is that the responses for the seniors and juniors are reversed.

Answer:

B. The responses for the seniors and juniors are reversed.