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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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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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.
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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