  ### Home > CC3 > Chapter 7 > Lesson 7.3.3 > Problem7-111

7-111.

Researchers have determined that teenagers’ memories are negatively affected by getting less than $10$ hours of sleep. Being good scientists, the math students at North Middle School were skeptical, so they did their own study. They asked $300$ students to memorize $10$ objects. The next day, each student was asked how much sleep they got and then was asked to list the ten items. The results are below.

Remembered all $\mathbf{10}$ items?

Yes

No

TOTAL

Less than $7$ hours sleep

$6$

$149$

$155$

$\mathbf{7}$ to $\mathbf{9}$ hours sleep

$11$

$109$

$120$

At least $\mathbf{10}$ hours sleep

$5$

$20$

$25$

TOTAL

$22$

$278$

$300$

Make a conditional relative frequency table to determine if there is an association between hours of sleep and memory.

In order to make a conditional relative frequency table, you must first decide which variable is independent and which is dependent.

Remembering depends on how many hours of sleep a student gets so the independent variable is hours of sleep.

The frequencies should be calculated based on row totals.

 Remembered all 10 items? Yes No Less than $\mathbf{7}$ hours sleep $\mathbf{3.9\%}$ $\mathbf{7}$ to $\mathbf{9}$ hours sleep $\mathbf{90.8\%}$ At least $\mathbf{10}$ hours sleep