Question

fill in the blank.
to test ( h_0: p = p_0 ) with the methods in this section, the values ( np_0 ) and ( n(1 - p_0) ) must both be at least (square).

Explanation:

Step1: Recall the condition for testing proportion

In hypothesis testing for a proportion \( H_0: p = p_0 \), when using the normal approximation to the binomial (which is the method in this section), the rule of thumb is that both \( np_0 \) and \( n(1 - p_0) \) should be at least 5 (or sometimes 10, but the common minimum is 5 for a rough approximation, and 10 for a better one; however, the standard answer here is 5).

Step2: Confirm the value

This is a standard condition for using the normal approximation to the binomial distribution in proportion hypothesis testing. So the value that both \( np_0 \) and \( n(1 - p_0) \) must be at least is 5 (or 10, but 5 is the more basic one taught initially).

Answer:

5 (or 10, but the most common answer here is 5)