
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Production Shifts and Quality Control Analysis**
A manufacturer of flash drives for data storage operates a production facility that runs on three eight-hour shifts per day.
The following contingency table shows the number of flash drives that were defective and not defective from each shift:
| Shift | Defective | Not Defective |
|------------|-----------|---------------|
| 7AM-3PM | 7 | 113 |
| 3PM-11PM | 10 | 90 |
| 11PM-7AM | 4 | 76 |
**Problem Statement:**
Using the given information, fill in the next two blanks.
If the two variables, shift and production quality, are independent, then the expected number of defective items for the 3PM-11PM shift is (without any decimal places):
**[First Blank for Answer]**
Given that this is an r×c table, what is the value for r?
**[Second Blank for Answer]** and what is the value of c? **[Third Blank for Answer]**
**Explanation:**
To calculate the expected number of defective items for the 3PM-11PM shift, we use the formula for expected frequency in a contingency table:
Expected frequency for a cell = (Row total × Column total) / Grand total
From the table:
- Total defective items = 7 + 10 + 4 = 21
- Total items in 3PM-11PM shift = 10 + 90 = 100
- Grand total of all items = (7 + 113) + (10 + 90) + (4 + 76) = 300
For the 3PM-11PM shift's defective items:
Expected number of defective items for 3PM-11PM shift = (100 × 21) / 300 = 7
The value for r (number of rows) and c (number of columns):
- Number of rows (r) = 3 (shifts)
- Number of columns (c) = 2 (defective, not defective)](https://content.bartleby.com/qna-images/question/7bf6b58d-ef43-404d-8e44-e8a8dab82f8c/9f5add2f-69cb-4a75-b27b-688ecaa6ab86/a7f0hob_thumbnail.jpeg)
Transcribed Image Text:**Production Shifts and Quality Control Analysis**
A manufacturer of flash drives for data storage operates a production facility that runs on three eight-hour shifts per day.
The following contingency table shows the number of flash drives that were defective and not defective from each shift:
| Shift | Defective | Not Defective |
|------------|-----------|---------------|
| 7AM-3PM | 7 | 113 |
| 3PM-11PM | 10 | 90 |
| 11PM-7AM | 4 | 76 |
**Problem Statement:**
Using the given information, fill in the next two blanks.
If the two variables, shift and production quality, are independent, then the expected number of defective items for the 3PM-11PM shift is (without any decimal places):
**[First Blank for Answer]**
Given that this is an r×c table, what is the value for r?
**[Second Blank for Answer]** and what is the value of c? **[Third Blank for Answer]**
**Explanation:**
To calculate the expected number of defective items for the 3PM-11PM shift, we use the formula for expected frequency in a contingency table:
Expected frequency for a cell = (Row total × Column total) / Grand total
From the table:
- Total defective items = 7 + 10 + 4 = 21
- Total items in 3PM-11PM shift = 10 + 90 = 100
- Grand total of all items = (7 + 113) + (10 + 90) + (4 + 76) = 300
For the 3PM-11PM shift's defective items:
Expected number of defective items for 3PM-11PM shift = (100 × 21) / 300 = 7
The value for r (number of rows) and c (number of columns):
- Number of rows (r) = 3 (shifts)
- Number of columns (c) = 2 (defective, not defective)
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