Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
\[
\begin{array}{l}
H_{0}: p=0.8 \text { versus } H_{1}: p> 0.8 \\
n=200 ; x=175, \alpha=0.05
\end{array}
\]
Is $n p_{0}\left(1-p_{0}\right) \geq 10$ ?
No
Yes

Step 1 ：The problem is asking to test the hypothesis using the P-value approach. The null hypothesis is that the proportion p is equal to 0.8, and the alternative hypothesis is that the proportion p is greater than 0.8. The sample size is 200 and the number of successes is 175. The significance level is 0.05.

Step 2 ：Before we can perform the test, we need to check if the sample size is large enough. The condition for this is that both np0 and n(1-p0) are greater than or equal to 10. Here, p0 is the proportion under the null hypothesis, which is 0.8 in this case.

Step 3 ：Calculate np0 and n(1-p0): np0 = 200 * 0.8 = 160.0, n(1-p0) = 200 * (1 - 0.8) = 40.0

Step 4 ：Both np0 and n(1-p0) are greater than 10. Therefore, the sample size is large enough to perform the test.

Step 5 ：\(\boxed{\text{Yes, } n p_{0}(1-p_{0}) \geq 10}\)