Question

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Explanation:

Identify the variables in the two-way table

The rows of the table represent the grade levels: "7th Grade" and "8th Grade". This corresponds to the variable "grade number" (or grade level).
The columns of the table represent the instruments being played: "Flute" and "Clarinet". This corresponds to the variable "type of instrument".

Evaluate the given options

• Option 1: "type of instrument and total number of seventh and eighth graders" — Incorrect, totals are summaries, not the categorical variables.
• Option 2: "type of instrument and total number of seventh graders" — Incorrect, totals are summaries.
• Option 3: "grade number and number of clarinet players" — Incorrect, "number of clarinet players" is a frequency count, not a variable.
• Option 4: "grade number and type of instrument" — Correct, these are the two categorical variables being compared.

Answer:

• (A) type of instrument and total number of seventh and eighth graders
• (B) type of instrument and total number of seventh graders
• (C) grade number and number of clarinet players
• (D) grade number and type of instrument (Correct answer)