Question

For a one-sample test for a population proportion p and sample size n, why is it necessary that np0 and n(1−p0) are both at least 10 ?.

Answer 1

Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.

What does the Central Limit Theorem states?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$.

From the equation of the standard error, we could see that if one of the conditions is not respected, the standard error would be very high, indicating a low accuracy of the estimate, hence it is found that these conditions are required to avoid the high variability associated with small samples.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213