Questions: Fill in the blank. To test (H0: p=p0) with the methods in this section, the values (n p0) and (n(1-p0)) must both be at least (square).

Transcript text: Fill in the blank. To test $H_{0}: p=p_{0}$ with the methods in this section, the values $n p_{0}$ and $n\left(1-p_{0}\right)$ must both be at least $\square$.

Solution

Solution Steps

Step 1: Understanding the Question

The question is asking for the minimum values that $ n p_{0} $ and $ n(1-p_{0}) $ must have in order to use certain statistical methods for hypothesis testing of a proportion $ p $.

Step 2: Applying the Rule of Thumb

In hypothesis testing for proportions, particularly when using the normal approximation to the binomial distribution, a common rule of thumb is that both $ n p_{0} $ and $ n(1-p_{0}) $ should be at least 5. This ensures that the sample size is large enough for the normal approximation to be valid.

Final Answer

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