The problem in the image is a hypothesis testing question using the P-value approach. You are asked to verify if the requirements of the test are satisfied by checking whether the product $np_0(1 - p_0) \geq 10$.

Let's break this down:

Given:

• Null Hypothesis ($H_0$): $p = 0.74$
• Alternative Hypothesis ($H_1$): $p \neq 0.74$
• Sample size $n = 500$
• Number of successes $x = 360$
• Significance level $\alpha = 0.01$
• $p_0 = 0.74$ (the hypothesized population proportion)

Step 1: Check $np_0(1 - p_0)$

We need to calculate:

$np_0(1 - p_0) = 500 \times 0.74 \times (1 - 0.74) = 500 \times 0.74 \times 0.26$

Step 2: Perform the Calculation

$np_0(1 - p_0) = 500 \times 0.74 \times 0.26 = 96.2$

Step 3: Compare with 10

Since $96.2 \geq 10$, the condition is satisfied.

Therefore, the correct answer would be Yes, because $np_0(1 - p_0) = 96.2$, which is greater than 10.

Let me know if you'd like further details on this!

Here are five related questions to expand your understanding:

1. How do you interpret the P-value in hypothesis testing?
2. What does it mean when a test fails to meet the requirement $np_0(1 - p_0) \geq 10$?
3. How is the test statistic calculated for hypothesis testing for proportions?
4. What is the role of the significance level $\alpha$ in hypothesis testing?
5. How do you compute the P-value for a two-tailed hypothesis test?

Tip: Always verify the assumptions and conditions of a hypothesis test before performing the calculations. This ensures the validity of the test results.