Evaluate the following formula for P, = 0.3, P₂=0.9, P₁-P₂=0, p=0.814232, q=0.110307, n, -80, and n₂ =97. (P₁-P₂)-(P₁-P₂) 2N p.q p.q n₁ n₂ + (Round to two decimal places as needed.)
Evaluate the following formula for P, = 0.3, P₂=0.9, P₁-P₂=0, p=0.814232, q=0.110307, n, -80, and n₂ =97. (P₁-P₂)-(P₁-P₂) 2N p.q p.q n₁ n₂ + (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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![**Evaluating a Statistical Formula for Proportions**
To assess the statistical significance of the difference between two sample proportions, we use the following formula for the z-score:
\[ z = \frac{\left( \hat{p_1} - \hat{p_2} \right) - \left( p_1 - p_2 \right)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}} \]
Given the values:
- \(\hat{p_1} = 0.3\)
- \(\hat{p_2} = 0.9\)
- \(p_1 - p_2 = 0\)
- \( \bar{p} = 0.814232\)
- \(\bar{q} = 0.110307\)
- \(n_1 = 80\)
- \(n_2 = 97\)
Substitute these values into the formula to calculate the z-score. Ensure that you round your final z-score value to two decimal places as needed.
The simplified formula for this specific problem is:
\[ z = \frac{(0.3 - 0.9) - 0}{\sqrt{\frac{0.814232 \times 0.110307}{80} + \frac{0.814232 \times 0.110307}{97}}} \]
Complete the calculations step-by-step to obtain the z-score.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39618134-6ceb-48ac-ab5a-e0c16873beed%2F3cdff9ab-aaef-4577-aca8-f583a39c1536%2Flmtxoh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluating a Statistical Formula for Proportions**
To assess the statistical significance of the difference between two sample proportions, we use the following formula for the z-score:
\[ z = \frac{\left( \hat{p_1} - \hat{p_2} \right) - \left( p_1 - p_2 \right)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}} \]
Given the values:
- \(\hat{p_1} = 0.3\)
- \(\hat{p_2} = 0.9\)
- \(p_1 - p_2 = 0\)
- \( \bar{p} = 0.814232\)
- \(\bar{q} = 0.110307\)
- \(n_1 = 80\)
- \(n_2 = 97\)
Substitute these values into the formula to calculate the z-score. Ensure that you round your final z-score value to two decimal places as needed.
The simplified formula for this specific problem is:
\[ z = \frac{(0.3 - 0.9) - 0}{\sqrt{\frac{0.814232 \times 0.110307}{80} + \frac{0.814232 \times 0.110307}{97}}} \]
Complete the calculations step-by-step to obtain the z-score.
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