## Engage NY Eureka Math 8th Grade Module 6 Lesson 14 Answer Key

### Eureka Math Grade 8 Module 6 Lesson 14 Exercise Answer Key

Example 1.
Suppose a random group of people are surveyed about their use of smartphones. The results of the survey are summarized in the tables below.

Example 2.
Suppose a sample of 400 participants (teachers and students) was randomly selected from the middle schools and high schools in a large city. These participants responded to the following question:

Which type of movie do you prefer to watch?
1. Action (The Avengers, Man of Steel, etc.)
2. Drama (42 (The Jackie Robinson Story), The Great Gatsby, etc.)
3. Science Fiction (Star Trek into Darkness, World War Z, etc.)
4. Comedy (Monsters University, Despicable Me 2, etc.)

Movie preference and status (teacher or student) were recorded for each participant.

Exercises 1–7

Exercise 1.
Two variables were recorded. Are these variables categorical or numerical?
Both variables are categorical.

Exercise 2.
The results of the survey are summarized in the table below.

a. What proportion of participants who are teachers prefer action movies?
$$\frac{40}{100}$$ = 0.40

b. What proportion of participants who are teachers prefer drama movies?
$$\frac{20}{100}$$ = 0.20

c. What proportion of participants who are teachers prefer science fiction movies?
$$\frac{10}{100}$$ = 0.10

d. What proportion of participants who are teachers prefer comedy movies?
$$\frac{30}{100}$$ = 0.30

The answers to Exercise 2 are called row relative frequencies. Notice that you divided each cell frequency in the Teacher row by the total for that row. Below is a blank relative frequency table.
Table of Row Relative Frequencies

Write your answers from Exercise 2 in the indicated cells in the table above.

Exercise 3.
Find the row relative frequencies for the Student row. Write your answers in the table above.
a. What proportion of participants who are students prefer action movies?
b. What proportion of participants who are students prefer drama movies?
c. What proportion of participants who are students prefer science fiction movies?
d. What proportion of participants who are students prefer comedy movies?
See the table above.

Exercise 4.
Is a participant’s status (i.e., teacher or student) related to what type of movie he would prefer to watch? Why or why not? Discuss this with your group.
No. Teachers are just as likely to prefer each movie type as students are, according to the row relative frequencies.

Exercise 5.
What does it mean when we say that there is no association between two variables? Discuss this with your group.
Answers will vary. No association means that knowing the value of one variable does not tell anything about the value of the other variable.

Exercise 6.
Notice that the row relative frequencies for each movie type are the same for both the Teacher and Student rows. When this happens, we say that the two variables, movie preference and status (student or teacher), are not associated. Another way of thinking about this is to say that knowing if a participant is a teacher (or a student) provides no information about his movie preference.
What does it mean if row relative frequencies are not the same for all rows of a two-way table?
It means that there is an association or a tendency between the two variables.

Exercise 7.
You can also evaluate whether two variables are associated by looking at column relative frequencies instead of row relative frequencies. A column relative frequency is a cell frequency divided by the corresponding column total.
For example, the column relative frequency for the Student/Action cell is $$\frac{120}{160}$$ = 0.75.
a. Calculate the other column relative frequencies, and write them in the table below.
Table of Column Relative Frequencies

Table of Column Relative Frequencies

b. What do you notice about the column relative frequencies for the four columns?
The column relative frequencies are equal for all four columns.

c. What would you conclude about association based on the column relative frequencies?
Because the column relative frequencies are the same for all four columns, we would conclude that there is no association between movie preference and status.

Example 3
In the survey described in Example 2, gender for each of the 400 participants was also recorded. Some results of the survey are given below:

• 160 participants preferred action movies.
• 80 participants preferred drama movies.
• 40 participants preferred science fiction movies.
• 240 participants were females.
• 78 female participants preferred drama movies.
• 32 male participants preferred science fiction movies.
• 60 female participants preferred action movies.

Exercises 8–15
Use the results from Example 3 to answer the following questions. Be sure to discuss these questions with your group members.

Exercise 8.
Complete the two-way frequency table that summarizes the data on movie preference and gender.

Exercise 9.
What proportion of the participants are female?
$$\frac{240}{400}$$ = 0.60

Exercise 10.
If there was no association between gender and movie preference, should you expect more females than males or fewer females than males to prefer action movies? Explain.
If there was no association between gender and movie preference, then I would expect more females than males to prefer action movies just because there are more females in the sample. However, if there was an association between gender and movie preference, then I would expect either fewer females than males who prefer action movies or considerably more females than males who prefer action movies.

Exercise 11.
Make a table of row relative frequencies of each movie type for the Male row and the Female row. Refer to Exercises 2–4 to review how to complete the table below.

Suppose that you randomly pick 1 of the 400 participants. Use the table of row relative frequencies on the previous page to answer the following questions.
Exercise 12.
If you had to predict what type of movie this person chose, what would you predict? Explain why you made this choice.
The participant likely prefers action movies because the largest proportion of participants preferred action movies.

Exercise 13.
If you know that the randomly selected participant is female, would you predict that her favorite type of movie is action? If not, what would you predict, and why?
No. A female participant is more likely to prefer comedy since it has the greatest row relative frequency in the Female row.

Exercise 14.
If knowing the value of one of the variables provides information about the value of the other variable, then there is an association between the two variables.
Is there an association between the variables gender and movie preference? Explain.
Yes. The row relative frequencies are not the same (not even close) in each row in the table.

Exercise 15.
What can be said when two variables are associated? Read the following sentences. Decide if each sentence is a correct statement based upon the survey data. If it is not correct, explain why not.
a. More females than males participated in the survey.
Correct

b. Males tend to prefer action and science fiction movies.
Correct

c. Being female causes one to prefer drama movies.
Incorrect Association does not imply a cause-and-effect relationship.

### Eureka Math Grade 8 Module 6 Lesson 14 Problem Set Answer Key

A sample of 200 middle school students was randomly selected from the middle schools in a large city. Answers to several survey questions were recorded for each student. The tables below summarize the results of the survey.
For each table, calculate the row relative frequencies for the Female row and for the Male row. Write the row relative frequencies beside the corresponding frequencies in each table below.

Question 1.
This table summarizes the results of the survey data for the two variables, gender and which sport the students prefer to play. Is there an association between gender and which sport the students prefer to play? Explain.

Yes, there appears to be an association between gender and sports preference. The row relative frequencies are not the same for the Male and the Female rows, as shown in the table above.

Question 2.
This table summarizes the results of the survey data for the two variables, gender and the students’ T-shirt sizes. Is there an association between gender and T-shirt size? Explain.

Yes, there appears to be an association between gender and T-shirt size. The row relative frequencies are not the same for the Male and the Female rows, as shown in the table above.

Question 3.
This table summarizes the results of the survey data for the two variables, gender and favorite type of music. Is there an association between gender and favorite type of music? Explain.

No, there does not appear to be an association between gender and favorite type of music. The row relative frequencies are about the same for the Male and Female rows, as shown in the table above.

### Eureka Math Grade 8 Module 6 Lesson 14 Exit Ticket Answer Key

A random sample of 100 eighth-grade students are asked to record two variables: whether they have a television in their bedrooms and if they passed or failed their last math test. The results of the survey are summarized below.

• 55 students have a television in their bedrooms.
• 35 students do not have a television in their bedrooms and passed their last math test.
• 25 students have a television and failed their last math test.
• 35 students failed their last math test.

Question 1.
Complete the two-way table.

Question 2.
Calculate the row relative frequencies, and enter the values in the table above. Round to the nearest thousandth.
The row relative frequencies are displayed in the table above.

Question 3.
Is there evidence of association between the variables? If so, does this imply there is a cause-and-effect relationship? Explain.