Evaluate the following formula for P₁ = 0.5, P2 = 0.1, P₁ P2 = 0, p=0.347407, q=0.802649, n₁ = 68, and n₂ = 82. (P1-P2)-(P1-P2) p.qp q n₁ n₂ Z= =(Round to two decimal places as needed.)
Evaluate the following formula for P₁ = 0.5, P2 = 0.1, P₁ P2 = 0, p=0.347407, q=0.802649, n₁ = 68, and n₂ = 82. (P1-P2)-(P1-P2) p.qp q n₁ n₂ Z= =(Round to two decimal places as needed.)
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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Q3
![### Evaluating a Statistical Formula
In this exercise, you are required to evaluate the given formula using provided parameters. The formula and parameters are typically used in hypothesis testing for comparing two proportions.
#### Given:
- \(\hat{p}_1 = 0.5\)
- \(\hat{p}_2 = 0.1\)
- \(p_1 = p_2 = 0\)
- \(\hat{p} = 0.347407\)
- \(\hat{q} = 0.802649\)
- \(n_1 = 68\)
- \(n_2 = 82\)
#### Formula:
\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1- p_2)}{\sqrt{\hat{p} \cdot \hat{q} \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \]
#### Calculations:
Calculate the value of \(z\) using the given data and the formula above.
- Ensure all calculations are rounded to two decimal places as needed.
- Input the final calculated value of \(z\) .
\[ z = \boxed{\quad} \]
*Note that in some educational settings, further detailed step-by-step instructions might be provided to reach the calculated value of \(z\).*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc18b90ea-cb53-41e6-9532-f9af83d8e951%2F523ac1ba-93fa-43b7-a25a-346aa8720010%2Fky3h1o_processed.png&w=3840&q=75)
Transcribed Image Text:### Evaluating a Statistical Formula
In this exercise, you are required to evaluate the given formula using provided parameters. The formula and parameters are typically used in hypothesis testing for comparing two proportions.
#### Given:
- \(\hat{p}_1 = 0.5\)
- \(\hat{p}_2 = 0.1\)
- \(p_1 = p_2 = 0\)
- \(\hat{p} = 0.347407\)
- \(\hat{q} = 0.802649\)
- \(n_1 = 68\)
- \(n_2 = 82\)
#### Formula:
\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1- p_2)}{\sqrt{\hat{p} \cdot \hat{q} \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \]
#### Calculations:
Calculate the value of \(z\) using the given data and the formula above.
- Ensure all calculations are rounded to two decimal places as needed.
- Input the final calculated value of \(z\) .
\[ z = \boxed{\quad} \]
*Note that in some educational settings, further detailed step-by-step instructions might be provided to reach the calculated value of \(z\).*
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