### 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} $.

a. The value of p̂ is obtained below: From the given information, n = 80 and X = 40. Thus, the…

Answered: In each case, find p and q. a. n 80 and…

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

### 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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