Statistically significant deviations from the mean

#1
I am preparing a submission to the Government in which I have to address unemployment levels in an area. The unemployment levels are obtained from Census data, and are calculated simply by dividing the number of unemployed in a community by the number in the labour-force of that community. I am looking at a small community in which unemployment is at a level of 9%. The average level for the State is 8.2%. Both of these statistics are obtained in the method described. My understanding is that the "average range" of a normal distribution is plus or minus one standard deviation from the mean. This may have been of some assistance if it were a valid assumption to make that the unemployment levels for all Statistical Local Areas in the State formed a normal distribution (and it may be - I'm not sure), and I knew the standard deviation for the unemployment levels of all of the communities - this would be a prohibitively time consuming exercise to work out. What I am trying to work out is what deviation from the mean is considered to be insignificant or within what would be considered the "average range" i.e. is .8% a significantly higher level of unemployment within the small community when compared to the unemployment level for the State.

About 18 years ago I did a first year subject in University in prob and stats, but the level of knowledge I have retained from that is quite basic. Thank you in advance for any assistance, or pointing me toward information sources where I may work it out for myself - I have been unable to find info on the net which matched the circumstances of my problem.
 

JohnM

TS Contributor
#2
This depends on a few factors, namely the actual difference between the proportions, the proportions themselves, and the sample size used to obtain the proportion.

This link will walk you through the steps necessary to test whether two proportions are significantly different:

http://davidmlane.com/hyperstat/B73479.html

The typical difference necessary for "significance" is around 2 standard deviations.
 
#3
Thankyou very much John. This was very helpful. Ultimately, the answer was not what I wanted to hear (that the difference in unemployment levels was significant), but I am sure that what I have learned from the link you provided will be of use to me quite often.