Question

To conduct a hypothesis test for one proportion, two requirements must be met. Suppose p = 1/10. What is the smallest n can be and both requirements still be met?

Answer 1

Answer:

To met both conditions, the smallest sample size n should be 50.

Step-by-step explanation:

To test a claim about proportion there are two requirements that must be met:

1) The sample observations are a simple random sample

2) The conditions for a binomial distribution are satisfied, that is:

$n\cdot p\geq 5\\\\n(1-p)\geq 5$

In this case, p=0.1, so first we have:

$n\cdot p \geq 5\\\\0.1n\geq5\\\\0.1n*10\geq 5*10\\\\n\geq 50$

Second,

$n\cdot (1-p) \geq 5\\\\0.9n\geq5\\\\n\geq 6$

To met both conditions, the smallest sample size n should be 50.