{"id":81636,"date":"2022-06-09T19:29:23","date_gmt":"2022-06-09T13:59:23","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=81636"},"modified":"2022-05-10T14:14:40","modified_gmt":"2022-05-10T08:44:40","slug":"eureka-math-grade-8-module-6-lesson-14","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-6-lesson-14\/","title":{"rendered":"Eureka Math Grade 8 Module 6 Lesson 14 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 6 Lesson 14 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 6 Lesson 14 Exercise Answer Key<\/h3>\n

Example 1.
\nSuppose a random group of people are surveyed about their use of smartphones. The results of the survey are summarized in the tables below.
\n\"Engage<\/p>\n

Example 2.
\nSuppose 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:<\/p>\n

Which type of movie do you prefer to watch?
\n1. Action (The Avengers, Man of Steel, etc.)
\n2. Drama (42 (The Jackie Robinson Story), The Great Gatsby, etc.)
\n3. Science Fiction (Star Trek into Darkness, World War Z, etc.)
\n4. Comedy (Monsters University, Despicable Me 2, etc.)<\/p>\n

Movie preference and status (teacher or student) were recorded for each participant.<\/p>\n

Exercises 1\u20137<\/p>\n

Exercise 1.
\nTwo variables were recorded. Are these variables categorical or numerical?
\nAnswer:
\nBoth variables are categorical.<\/p>\n

Exercise 2.
\nThe results of the survey are summarized in the table below.
\n\"Engage
\na. What proportion of participants who are teachers prefer action movies?
\nAnswer:
\n\\(\\frac{40}{100}\\) = 0.40<\/p>\n

b. What proportion of participants who are teachers prefer drama movies?
\nAnswer:
\n\\(\\frac{20}{100}\\) = 0.20<\/p>\n

c. What proportion of participants who are teachers prefer science fiction movies?
\nAnswer:
\n\\(\\frac{10}{100}\\) = 0.10<\/p>\n

d. What proportion of participants who are teachers prefer comedy movies?
\nAnswer:
\n\\(\\frac{30}{100}\\) = 0.30<\/p>\n

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.
\nTable of Row Relative Frequencies
\n\"Engage
\nAnswer:
\n\"Engage<\/p>\n

Write your answers from Exercise 2 in the indicated cells in the table above.<\/p>\n

Exercise 3.
\nFind the row relative frequencies for the Student row. Write your answers in the table above.
\na. What proportion of participants who are students prefer action movies?
\nb. What proportion of participants who are students prefer drama movies?
\nc. What proportion of participants who are students prefer science fiction movies?
\nd. What proportion of participants who are students prefer comedy movies?
\nAnswer:
\nSee the table above.<\/p>\n

Exercise 4.
\nIs a participant\u2019s 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.
\nAnswer:
\nNo. Teachers are just as likely to prefer each movie type as students are, according to the row relative frequencies.<\/p>\n

Exercise 5.
\nWhat does it mean when we say that there is no association between two variables? Discuss this with your group.
\nAnswer:
\nAnswers will vary. No association means that knowing the value of one variable does not tell anything about the value of the other variable.<\/p>\n

Exercise 6.
\nNotice 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.
\nWhat does it mean if row relative frequencies are not the same for all rows of a two-way table?
\nAnswer:
\nIt means that there is an association or a tendency between the two variables.<\/p>\n

Exercise 7.
\nYou 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.
\nFor example, the column relative frequency for the Student\/Action cell is \\(\\frac{120}{160}\\) = 0.75.
\na. Calculate the other column relative frequencies, and write them in the table below.
\nTable of Column Relative Frequencies
\n\"Engage
\nAnswer:
\nTable of Column Relative Frequencies
\n\"Engage<\/p>\n

b. What do you notice about the column relative frequencies for the four columns?
\nAnswer:
\nThe column relative frequencies are equal for all four columns.<\/p>\n

c. What would you conclude about association based on the column relative frequencies?
\nAnswer:
\nBecause the column relative frequencies are the same for all four columns, we would conclude that there is no association between movie preference and status.<\/p>\n

Example 3
\nIn the survey described in Example 2, gender for each of the 400 participants was also recorded. Some results of the survey are given below:<\/p>\n