Answered: In a study of factors that influence…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

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$**Title: Understanding Factors Influencing Brand Switching** **Introduction:** In a study of factors that influence brand switching by a certain demographic, the following factors were identified as significant based on the responses of the 439 participants in the survey: 1. Better price 2. Friend's recommendation 3. Seeing others use it 4. Interesting packaging 5. Buzz—people talking about the brand 6. An advertisement 7. Press stories 8. Entertainer/sports celebrity endorsement **Survey Results:** The results of the survey are shown in the table below: | Factor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |--------|------|-------|-------|-------|-------|-------|-------|-------| | Respondents (%) | 68.8 | 60.4 | 22.8 | 20.8 | 16.8 | 14.7 | 6.7 | **Questions:** Consider the following definitions: - Let $ A $ denote the set of factors that had a response greater than 20%. - Let $ B $ denote the set of factors that had a response between 15% and 25%. - Let $ C $ denote the set of factors that had a response less than 25%. Based on these definitions, answer the following questions: (a) Determine $n(A)$, $n(B)$, and $n(C)$. $ n(A) = $ $ n(B) = $ $ n(C) = $ (b) Compute $ n(A \cap B) $. $ n(A \cap B) = $ (c) Compute $ n(A^c \cap C) $. $ n(A^c \cap C) = $ (d) Compute $ n(A \cap B^c) $. $ n(A \cap B^c) = $ (e) Compute $ n(A^c \cap C^c) $. $ n(A^c \cap C^c) = $ (f) Compute $ n[(A \cup B) \cap C] $. $ n[(A \cup B) \cap C] = $ --- **Graph/Diagram Explanation:** The provided table categorizes the$

Transcribed Image Text:**Title: Understanding Factors Influencing Brand Switching** **Introduction:** In a study of factors that influence brand switching by a certain demographic, the following factors were identified as significant based on the responses of the 439 participants in the survey: 1. Better price 2. Friend's recommendation 3. Seeing others use it 4. Interesting packaging 5. Buzz—people talking about the brand 6. An advertisement 7. Press stories 8. Entertainer/sports celebrity endorsement **Survey Results:** The results of the survey are shown in the table below: | Factor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |--------|------|-------|-------|-------|-------|-------|-------|-------| | Respondents (%) | 68.8 | 60.4 | 22.8 | 20.8 | 16.8 | 14.7 | 6.7 | **Questions:** Consider the following definitions: - Let $ A $ denote the set of factors that had a response greater than 20%. - Let $ B $ denote the set of factors that had a response between 15% and 25%. - Let $ C $ denote the set of factors that had a response less than 25%. Based on these definitions, answer the following questions: (a) Determine $n(A)$, $n(B)$, and $n(C)$. $ n(A) = $ $ n(B) = $ $ n(C) = $ (b) Compute $ n(A \cap B) $. $ n(A \cap B) = $ (c) Compute $ n(A^c \cap C) $. $ n(A^c \cap C) = $ (d) Compute $ n(A \cap B^c) $. $ n(A \cap B^c) = $ (e) Compute $ n(A^c \cap C^c) $. $ n(A^c \cap C^c) = $ (f) Compute $ n[(A \cup B) \cap C] $. $ n[(A \cup B) \cap C] = $ --- **Graph/Diagram Explanation:** The provided table categorizes the

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