Hypothesis testing

What do you mean by 'actual ratio'?

 

I'm a bit confused by your question but if I'm understanding it right:

You have two assumptions here: First you have a normal population or large sample and second, the population deviation is known.

State your null and alternative hypothesis.

H₀: mu is equal to 20%
H_A: mu is not equal to 20%

Because you are dealing with the alternative hypothesis that is not equal to mu naught, you will have a two tailed test with the Reject H₀ in the two tails and the Do Not Reject H₀ in the middle of the curve.

Now, you compute the value of the test statistic:

z = (sample mean - mu naught)/[(population deviation)(sample size)^(1/2)]

I assume you are using a significance level of 5% but since you are dealing with a two tailed test, divide that area by two (in this case, 0.05/2). Essentially, this is the area you will be looking for in the table of z scores in the appendix of any Statistics book.

I don't have a book with me at the moment but look up the z score that corresonds to your significance level. If the test statistic falls in the Do Not Reject H₀, obviously, don't reject H₀. Likewise, if it falls in the reject zone, reject H₀.

Hope this helps.

 

A bit of an embellishment to my earlier post:

The z score corresponding to your significance level is the numerical "mark" of where the Do not reject/ reject regions are.