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:
[tex]n\cdot p\geq 5\\\\n(1-p)\geq 5[/tex]
In this case, p=0.1, so first we have:
[tex]n\cdot p \geq 5\\\\0.1n\geq5\\\\0.1n*10\geq 5*10\\\\n\geq 50[/tex]
Second,
[tex]n\cdot (1-p) \geq 5\\\\0.9n\geq5\\\\n\geq 6[/tex]
To met both conditions, the smallest sample size n should be 50.
