In each case, find p and q. a. n 80 and X = 40 %3D %3D b. n = 200 and X = 90 %3D %D C. n = 130 and X = 60 p = d. 25 % е. 42% = || I|

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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### Task: Calculate \( \hat{p} \) and \( \hat{q} \)

In this exercise, you are asked to find the values of \( \hat{p} \) and \( \hat{q} \) for each given scenario. Here’s how you approach this task:

#### Formula:
- \( \hat{p} = \frac{X}{n} \)
- \( \hat{q} = 1 - \hat{p} \)

#### Scenarios:

**a.** \( n = 80 \) and \( X = 40 \)
- \( \hat{p} = \) [ ]
- \( \hat{q} = \) [ ]

**b.** \( n = 200 \) and \( X = 90 \)
- \( \hat{p} = \) [ ]
- \( \hat{q} = \) [ ]

**c.** \( n = 130 \) and \( X = 60 \)
- \( \hat{p} = \) [ ]
- \( \hat{q} = \) [ ]

**d.** Given \( 25\% \)
- \( \hat{p} = \) [ ]
- \( \hat{q} = \) [ ]

**e.** Given \( 42\% \)
- \( \hat{p} = \) [ ]
- \( \hat{q} = \) [ ]

### Explanation:

For each case:

- **Calculate \( \hat{p} \):** This represents the sample proportion, calculated by dividing \( X \) (the number of successes) by \( n \) (the total number).
  
- **Calculate \( \hat{q} \):** This is the complement of \( \hat{p} \), found by subtracting \( \hat{p} \) from 1.

For scenarios **d** and **e**, the percentages represent direct values for \( \hat{p} \), so convert them into decimal form (e.g., \( 25\% = 0.25 \)) and find \( \hat{q} = 1 - \hat{p} \).
Transcribed Image Text:### Task: Calculate \( \hat{p} \) and \( \hat{q} \) In this exercise, you are asked to find the values of \( \hat{p} \) and \( \hat{q} \) for each given scenario. Here’s how you approach this task: #### Formula: - \( \hat{p} = \frac{X}{n} \) - \( \hat{q} = 1 - \hat{p} \) #### Scenarios: **a.** \( n = 80 \) and \( X = 40 \) - \( \hat{p} = \) [ ] - \( \hat{q} = \) [ ] **b.** \( n = 200 \) and \( X = 90 \) - \( \hat{p} = \) [ ] - \( \hat{q} = \) [ ] **c.** \( n = 130 \) and \( X = 60 \) - \( \hat{p} = \) [ ] - \( \hat{q} = \) [ ] **d.** Given \( 25\% \) - \( \hat{p} = \) [ ] - \( \hat{q} = \) [ ] **e.** Given \( 42\% \) - \( \hat{p} = \) [ ] - \( \hat{q} = \) [ ] ### Explanation: For each case: - **Calculate \( \hat{p} \):** This represents the sample proportion, calculated by dividing \( X \) (the number of successes) by \( n \) (the total number). - **Calculate \( \hat{q} \):** This is the complement of \( \hat{p} \), found by subtracting \( \hat{p} \) from 1. For scenarios **d** and **e**, the percentages represent direct values for \( \hat{p} \), so convert them into decimal form (e.g., \( 25\% = 0.25 \)) and find \( \hat{q} = 1 - \hat{p} \).
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