MATLAB: An Introduction with Applications
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)
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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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