---### Evaluating a Z-Score Formula for Two ProportionsIn this example, we will evaluate the z-score formula for the difference between two population proportions. The formula to calculate the z-score is given by:\[ z = \frac{\left(\hat{p}_1 - \hat{p}_2 \right) - \left(p_1 - p_2 \right)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \]We have the following values:* $\hat{p}_1 = 0.3$* $\hat{p}_2 = 0.7$* $p_1 - p_2 = 0$* $\hat{p} = 0.709891$* $\hat{q} = 0.266566$* $n_1 = 74$* $n_2 = 88$To simplify, replace the values into the formula:\[ z = \frac{\left(0.3 - 0.7 \right) - 0}{\sqrt{\frac{0.709891 \cdot 0.266566}{74} + \frac{0.709891 \cdot 0.266566}{88}}} \]Proceed to calculate the inner values step by step:1. Calculate the difference in sample proportions: \[ \hat{p}_1 - \hat{p}_2 = 0.3 - 0.7 = -0.4 \]2. Since $ p_1 - p_2 = 0 $, the numerator becomes: \[ -0.4 - 0 = -0.4 \]3. Calculate $ \frac{\hat{p} \cdot \hat{q}}{n_1} $ and $ \frac{\hat{p} \cdot \hat{q}}{n_2} $: \[ \frac{0.709891 \cdot 0.266566}{74} \] \[ \frac{0.709891 \cdot 0.266566}{88} \]4. Sum these two results for the denominator and compute the square

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Description: ---### Evaluating a Z-Score Formula for Two ProportionsIn this example, we will evaluate the z-score formula for the difference between two population proportions. The formula to calculate the z-score is given by:\[ z = \frac{\left(\hat{p}_1 - \hat{

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Evaluate the following formula for p, = 0.3, P2 = 0.7, p, - P2 = 0, p = 0.709891, q = 0.266566, n, = 74, and n2 = 88. (Pi - P2) - (P1 -P2) z= p•q, p•q n2 (Round to two decimal places as needed.)

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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### Evaluating a Z-Score Formula for Two Proportions

In this example, we will evaluate the z-score formula for the difference between two population proportions. The formula to calculate the z-score is given by:

\[ z = \frac{\left(\hat{p}_1 - \hat{p}_2 \right) - \left(p_1 - p_2 \right)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \]

We have the following values:
* $\hat{p}_1 = 0.3$
* $\hat{p}_2 = 0.7$
* $p_1 - p_2 = 0$
* $\hat{p} = 0.709891$
* $\hat{q} = 0.266566$
* $n_1 = 74$
* $n_2 = 88$

To simplify, replace the values into the formula:

\[ z = \frac{\left(0.3 - 0.7 \right) - 0}{\sqrt{\frac{0.709891 \cdot 0.266566}{74} + \frac{0.709891 \cdot 0.266566}{88}}} \]

Proceed to calculate the inner values step by step:

1. Calculate the difference in sample proportions:
\[ \hat{p}_1 - \hat{p}_2 = 0.3 - 0.7 = -0.4 \]

2. Since $ p_1 - p_2 = 0 $, the numerator becomes:
\[ -0.4 - 0 = -0.4 \]

3. Calculate $ \frac{\hat{p} \cdot \hat{q}}{n_1} $ and $ \frac{\hat{p} \cdot \hat{q}}{n_2} $:
\[ \frac{0.709891 \cdot 0.266566}{74} \]
\[ \frac{0.709891 \cdot 0.266566}{88} \]

4. Sum these two results for the denominator and compute the square

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