Lesson 7.3.3
HW: 7-110 to 7-115
Learning Target: Scholars will informally look for and describe associations between two categorical
variables in two-way tables. They will develop understanding that association can be seen in table rows
or in table columns.
In previous lessons, you described the association between two numerical variables, such as the amount
of fertilizer used and the height of the plant. Some variables, however – such as gender, eye color, names
of countries, or weather conditions – are not numerical. Since the data are in categories, non-numerical
variables are called categorical variables. Another type of categorical variable occurs when numerical
variables are lumped into categories, such as in age groups. Today you will look for relationships in
variables that are not numerical.
7-107. The experiments students did with plants and different growing conditions in Lesson 7.1.3 caught
the attention of a local farmer. He was interested in whether the type of soil made a difference in the
height of his corn crop. He planted 2500 stalks of corn and collected the following data. This type of
table is called a frequency table because it shows counts, or frequencies, in each of the cells of the table.
1. Make a conjecture about the effect of soil type on the height of the corn.
2. The table of data on corn height used counts because it counted the number of stalks of
corn. When analyzing categorical data, percents are much easier to analyze. But first,
you need to determine the independent variable so that you can determine, “Percent of
what?” What is the independent variable in this situation?
3. Create a second table that contains the data above but as percentages instead of
counts. The percentage should be the count for each height category out of the total
number for that soil type. For example, the height of the bar for 0-3 ft will be 9.0%,
because
is 0.090. The third row of the table is not needed in this case.
7-108. The farmer is interested in the height of his corn for each of the two soil types. A straightforward
way to compare the effect of the independent variable is to make a different bar graph for each
independent variable.
4. Make a bar graph for the sandy soil. The horizontal axis should be the height
categories. The vertical axis will represent the percent of the corn in sandy soil that grew
to that height.
5. Make a similar bar graph for the other independent variable.
6. Is the height of corn associated with the soil type? That is, does the soil type have an
impact on height? Report your conclusions to the farmer.
7. Why did you make a bar graph instead of a histogram for the height of the corn?
7-109. The nutrition staff at CPM Diabetic Institute is interested in the impact of three new energy bars on
blood sugar levels. The staff conducted a study on 1000 volunteers and collected the following data.
8. Complete the table by computing row and column totals. What is the independent
variable?
9. A relative frequency table displays the percents in a table instead of a bar
graph. Change the frequency table at the beginning of this problem to a relative
frequency table by changing the counts to percents. For example, the 30 Mighty Bars
that lowered blood sugar will be displayed as 20%.
10. Use your data from the relative frequency table to make a bar graph for each of the
independent variables. The horizontal axis should be the dependent variable.
11. Is there an association between blood sugar level and the choice of energy bar?
7-110. An unusually severe increase in gasoline prices may have motivated full-sized pickup truck buyers
to purchase a highly fuel-efficient vehicle. Purchase behavior was collected in one area for one year and
reported below.
1. Complete the row and column totals. What is the independent variable?
2. Create a relative frequency table. Is there an association between fuel prices and the
number of highly fuel-efficient trucks purchased?
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 he or she got and then was asked to list the ten items. The results are below.
Make a relative frequency table to determine if there is an association between hours of sleep and
memory.
7-112. Ruthie did a survey among her classmates comparing the time
spent playing video games to the time spent studying. The scatterplot of her data is shown at right.
1. What association can you make from her data?
2. Use an ordered pair (x, y) to identify any outliers.
7-113. Sao can text 1500 words per hour. He needs to text a message with 85 words. He only has 5
minutes between classes to complete the text. Can he do it in 5 minutes?
7-114. Where would the point (11, −18) be after each transformation described below?
3. Reflect (11, −18) across the x-axis, and then reflect that point across the y-axis.
4. Translate (11, −18) 5 units to the right and 3 units down.
7-115. This problem is a checkpoint for solving equations with fractions and decimals (Fraction
Busters). It will be referred to as Checkpoint 7.

Solve each equation or system of equations.
1.
x+ x=2
2. x + 0.15x = $2
3.
4. y =
y=
x+8
x + 10
Lesson 7.3.3

7-107.
1.
2.
3.

7-108. See below:
See below:
Answers will vary.
The type of soil.
See answer table below.
2. Possible bar graphs are below.

3. For the clay soil, there was a roughly equal percentage of stalks for each height;
however, for the sandy soil, there were many more tall stalks than short ones; the
height of the stalks is not independent of the soil type, so there is an association
between soil type and height of corn; assuming this was an appropriately
randomized controlled experiment, if the farmer wants taller stalks, he should use
sandy soil.
4. The heights are in categories; to make a histogram the bin widths would need to
be equal, say 0-2 ft., 3-5 ft., etc.; note that in a bar graph the bars do not touch
each other, while in a histogram they do touch.
7-109. See below:
2. Row totals: 187, 813. Column totals 150, 500, 350. The type of energy bar.
3. See solutions in table below.
4. See bar graphs below.
5. No association, each of the energy bars raises blood sugar in about 81% of the
volunteers.

7-110. See below:
1. Number of Highly Fuel Efficient Trucks Purchased: 834; Regular
Trucks Purchased: 79184; Low Fuel Prices: 37321; High Fuel Prices:
42697; Fuel prices
2. See the relative frequency table below. There does not appear to be an
association; only about 1% of cars are fuel efficient, regardless of whether prices
are high or low.

7-111. See table below; the independent variable is the hours of sleep; there is an
association; as the number of hours of sleep increases, a higher percent of the students
remember all ten items.

7-112. See below:
1. Moderate negative association
2. (100, 140)

7-113. Yes, 1500 wph = 25 words per minute; he can text 125 words in 5 minutes.

7-114. See below:
1. (−11, 18)
2. (16, −21)

7-115. See below:
1. x =
=3
2. x =
≈ $1.74
3. x = −5
4. x = 12, y = 16