Homework: Set - Prerequisite Week 6 Homework Check here for instructional material to complete this problem. Evaluate the following formula for P₁ - P₂ (P₁-P₂)-(P₁-P₂) Z= Z= p.q n₁ + p.q П2 = 0, p=0.164948, q=1-p, x₁ =79, x₂ = 17, ₁ (Round to two decimal places as needed.) Question 2, IR.9.4 > = 295, n₂ = 287, P₁ = X₁ and P2 n₁ 1₂
Homework: Set - Prerequisite Week 6 Homework Check here for instructional material to complete this problem. Evaluate the following formula for P₁ - P₂ (P₁-P₂)-(P₁-P₂) Z= Z= p.q n₁ + p.q П2 = 0, p=0.164948, q=1-p, x₁ =79, x₂ = 17, ₁ (Round to two decimal places as needed.) Question 2, IR.9.4 > = 295, n₂ = 287, P₁ = X₁ and P2 n₁ 1₂
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
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 for instructional material to complete this problem.
---
#### Evaluate the following formula for:
\[ p_1 - p_2 = 0 \]
\[ \bar{p} = 0.164948, \quad \bar{q} = 1 - \bar{p} \]
\[ x_1 = 79, \quad x_2 = 17 \]
\[ n_1 = 295, \quad n_2 = 287 \]
\[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \]
\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}}
\]
\[
z = \boxed{\ \ \ \ \ \ \ \ \ \ \ } \quad \text{(Round to two decimal places as needed.)}
\]
---
**Explanation of the Formula:**
1. **\( \hat{p}_1 \) and \( \hat{p}_2 \)**: These are sample proportions calculated as:
\[
\hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2}
\]
where \( x_1 \) and \( x_2 \) are the number of successes in each sample, and \( n_1 \) and \( n_2 \) are the sample sizes.
2. **\( \bar{p} \) and \( \bar{q} \)**: These are the pooled sample proportion and its complement.
\[
\bar{q} = 1 - \bar{p}
\]
3. **Z-Score Calculation**:
\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5df71d79-be11-47b2-8651-31f6c3899472%2Fbfb4aa37-4dc3-45d0-a385-b3078434b095%2F3v5eqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Homework: Set - Prerequisite Week 6
**Question 2, IR.9.4**
Check [here](#) for instructional material to complete this problem.
---
#### Evaluate the following formula for:
\[ p_1 - p_2 = 0 \]
\[ \bar{p} = 0.164948, \quad \bar{q} = 1 - \bar{p} \]
\[ x_1 = 79, \quad x_2 = 17 \]
\[ n_1 = 295, \quad n_2 = 287 \]
\[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \]
\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}}
\]
\[
z = \boxed{\ \ \ \ \ \ \ \ \ \ \ } \quad \text{(Round to two decimal places as needed.)}
\]
---
**Explanation of the Formula:**
1. **\( \hat{p}_1 \) and \( \hat{p}_2 \)**: These are sample proportions calculated as:
\[
\hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2}
\]
where \( x_1 \) and \( x_2 \) are the number of successes in each sample, and \( n_1 \) and \( n_2 \) are the sample sizes.
2. **\( \bar{p} \) and \( \bar{q} \)**: These are the pooled sample proportion and its complement.
\[
\bar{q} = 1 - \bar{p}
\]
3. **Z-Score Calculation**:
\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar
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