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.