Question

How do I find the Z score for a statistic without standard deviation given Pop mean=.05%, n=100, Sample mean of .11%?

Answer 1

By definition, Z score is:
`z=(x-mu)/sigma`
where `x` is your datum, `mu` is the mean of your population and `sigma` is its standard deviation. Basically, it's a measure of deviation from the mean in units of standard deviation.

Unless I misunderstood your problem, I see no way you can calculate this number without knowing a standard deviation.

Answer 2

I think the problem is really about a proportion so you do not need the standard deviation to find the standardized test statistic z. See the Explanation for the formula.

Explanation:

In your question, the sample proportion (p-hat) is 0.11%. The population proportion, p, is 0.05%. Use the following procedure: