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.