Learn by Doing – Proportions (Step 2) Understanding the Test Statistic
Consider the population of part-time college students. Suppose that 60% of this population is female.
Here is the sampling distribution for the proportion of females in random samples of n students. The standard deviation is approximately 0.10. Lines indicate a distance of 1 and 2 standard deviations above and below the mean.
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12017_prop2.swf
Here is the sampling distribution for the proportion of supporters in random samples of 25 adults. The standard deviation is approximately 0.10.
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12018_prop2.swf
If we increase the sample size to 100, the standard deviation decreases to approximately 0.05, as shown.
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12019_prop2.swf
This document is linked from Proportions (Step 2).