Siven the contingency table shown here, find P(WnS. Cell Phone Service Provider County Macomb (M) Oakland (0) Sprint (S) AT&T (A) Verizon (V) Row Total 17 25 8 50 19 38 13 70 Wayne (W) 24 37 19 80 Col Total 60 100 40 200
Siven the contingency table shown here, find P(WnS. Cell Phone Service Provider County Macomb (M) Oakland (0) Sprint (S) AT&T (A) Verizon (V) Row Total 17 25 8 50 19 38 13 70 Wayne (W) 24 37 19 80 Col Total 60 100 40 200
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Analyzing a Contingency Table
Given the contingency table shown here, find \( P(W \mid N_S) \).
#### Contingency Table: Cell Phone Service Provider
| County | Sprint (S) | AT&T (A) | Verizon (V) | Row Total |
|------------|------------|----------|-------------|-----------|
| Macomb (M) | 17 | 25 | 8 | 50 |
| Oakland (O)| 19 | 38 | 13 | 70 |
| Wayne (W) | 24 | 37 | 19 | 80 |
| **Col Total** | **60** | **100** | **40** | **200** |
#### Explanation
- **Rows**: Represent different counties: Macomb, Oakland, and Wayne.
- **Columns**: Represent different cell phone service providers: Sprint, AT&T, and Verizon.
- **Row and Column Totals**: Sum of the values in each row and column, respectively.
#### Calculation for \( P(W \mid N_S) \)
To find the probability of Wayne County given that a user is not with Sprint (\( N_S \)), use:
\[ P(W \mid N_S) = \frac{\text{Wayne, Not Sprint Total}}{\text{Total Not Sprint}} \]
**Wayne, Not Sprint Total:**
- AT&T in Wayne: 37
- Verizon in Wayne: 19
\[ \text{Wayne, Not Sprint Total} = 37 + 19 = 56 \]
**Total Not Sprint:**
- Column Total for AT&T and Verizon: \( 100 + 40 = 140 \)
\[ P(W \mid N_S) = \frac{56}{140} = 0.40 \]
### Multiple Choice
- \(\bigcirc\) 0.58
- \(\bigcirc\) 0.12
- \(\bigcirc\) 0.40
- \(\bigcirc\) 0.30
**Correct Answer:** 0.40
This problem explores using a contingency table to calculate conditional probabilities, a fundamental concept in statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadb882f8-f4be-49b7-a475-a003823b1c8d%2F9e522910-4f0a-4461-a6b1-87859a30dc82%2Fkijnc69_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing a Contingency Table
Given the contingency table shown here, find \( P(W \mid N_S) \).
#### Contingency Table: Cell Phone Service Provider
| County | Sprint (S) | AT&T (A) | Verizon (V) | Row Total |
|------------|------------|----------|-------------|-----------|
| Macomb (M) | 17 | 25 | 8 | 50 |
| Oakland (O)| 19 | 38 | 13 | 70 |
| Wayne (W) | 24 | 37 | 19 | 80 |
| **Col Total** | **60** | **100** | **40** | **200** |
#### Explanation
- **Rows**: Represent different counties: Macomb, Oakland, and Wayne.
- **Columns**: Represent different cell phone service providers: Sprint, AT&T, and Verizon.
- **Row and Column Totals**: Sum of the values in each row and column, respectively.
#### Calculation for \( P(W \mid N_S) \)
To find the probability of Wayne County given that a user is not with Sprint (\( N_S \)), use:
\[ P(W \mid N_S) = \frac{\text{Wayne, Not Sprint Total}}{\text{Total Not Sprint}} \]
**Wayne, Not Sprint Total:**
- AT&T in Wayne: 37
- Verizon in Wayne: 19
\[ \text{Wayne, Not Sprint Total} = 37 + 19 = 56 \]
**Total Not Sprint:**
- Column Total for AT&T and Verizon: \( 100 + 40 = 140 \)
\[ P(W \mid N_S) = \frac{56}{140} = 0.40 \]
### Multiple Choice
- \(\bigcirc\) 0.58
- \(\bigcirc\) 0.12
- \(\bigcirc\) 0.40
- \(\bigcirc\) 0.30
**Correct Answer:** 0.40
This problem explores using a contingency table to calculate conditional probabilities, a fundamental concept in statistics.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman