The calculated \( z \)-value is approximately **5.28**. 

This value is used to determine the significance of the difference between the two proportions.

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### Related Questions:
1. How does the \( z \)-value affect the P-value?
2. Why is a higher \( z \)-value associated with a smaller P-value?
3. What would the \( z \)-value be if the proportions were closer?
4. How is the pooled proportion \( \hat{p} \) derived?
5. What happens if the sample sizes are different?
6. How does changing the significance level affect the hypothesis test?
7. Can the \( z \)-value be negative? What would that indicate?
8. How would a confidence interval be affected by the \( z \)-value?

**Tip**: The \( z \)-value is critical in determining whether to reject the null hypothesis; the larger the \( z \)-value, the stronger the evidence against the null hypothesis.

Explore the significance of the Z-value in hypothesis testing with a detailed explanation of its calculation and impact. Learn how the Z-value of 5.28 determines the difference between proportions and influences the P-value. Useful insights for advanced undergraduate students and researchers.

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