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The image contains a hypothesis test question using the P-value approach. Here's a breakdown of the problem:

- **Hypotheses**:
  - \( H_0 \): \( p = 0.79 \)
  - \( H_1 \): \( p \neq 0.79 \)

- **Given data**:
  - Sample size: \( n = 500 \)
  - Successes: \( x = 380 \)
  - Significance level: \( \alpha = 0.01 \)

- **Requirement check**:
  The question asks to verify if the condition \( np_0(1 - p_0) \geq 10 \) is satisfied, where \( p_0 = 0.79 \).

### Calculation:
1. \( n = 500 \)
2. \( p_0 = 0.79 \)
3. \( 1 - p_0 = 1 - 0.79 = 0.21 \)

Now calculate:
\[
np_0(1 - p_0) = 500 \times 0.79 \times 0.21 = 500 \times 0.1659 = 82.95
\]

Since \( 82.95 \geq 10 \), the condition is met.

### Conclusion:
- The correct answer is **Option A**: "Yes, because \( np_0(1 - p_0) = 82.95 \)."

Would you like further details or explanations?

Here are five related questions:
1. What is the next step after verifying the condition \( np_0(1 - p_0) \geq 10 \) in a hypothesis test?
2. How do you calculate the test statistic for this hypothesis test?
3. What is the role of the significance level \( \alpha = 0.01 \) in hypothesis testing?
4. How do you interpret the P-value in hypothesis testing?
5. What is the difference between a one-tailed and a two-tailed hypothesis test?

**Tip**: Always ensure that the condition \( np_0(1 - p_0) \geq 10 \) is checked before proceeding with normal approximation in hypothesis testing.

Test the hypothesis using the P-value approach. H₀: p = 0.79 versus H₁: p ≠ 0.79. n = 500, x = 380, α = 0.01. Is np₀(1 - p₀) ≥ 10?

Solve the hypothesis test using the P-value approach for H₀: p = 0.79 versus H₁: p ≠ 0.79 with sample size n = 500, successes x = 380, and significance level α = 0.01. Verify the condition np₀(1 - p₀) ≥ 10, using np₀ = 82.95.

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