Hypothesis Testing Question, need assistance after trying...

#1
Hello Everyone,

The question is this:

A medical researcher claims that at least 23% of U.S. adults are smokers. In a random sample of 200 U.S. adults, 22.5% say that they are smokers. At the .01 level of significance, is there enough evidence to reject the researcher's claim?

I found .0297 to be the standard deviation. Hope that is right.

I drew the diagram with .23 as the mean and I was trying to find the critical value by going .23 + Z(.0297) I could not decide if that was the right equation and I did not know how to determine the Z that I need to use.

Any assistance on this would be wonderful. I am so lost on this one.

Thank you.
 
#2
Your null hypothesis:
both samples come from the same population.
That is your sample of two hundered with 22.5% smokers
and the researchers sample with 23% smokers.

We need the standard error. That is the standard deviation of the sample.
you need to multiply the SD by sqrt(200)

z=(46-45)/(sd/sqrt(200)) ;note all units are converted to numbers from %

I am not sure if you have calculated your sd correctly. So I will go by
by an example. if say your z=-2, then we know the mean of our sample
falls in the tail end of the normal curve. This is where only 2.5% of the samples lie.

Therefore the conclusion is that there is 2.5% chance that the researcher's claim is true. In other words, there is a 97.5% chance his claim is wrong.
Hope this gives you some idea.

bbkaran